Add your flour and the larger amount of sugar to a medium-sized mixing bowl and whisk them together. Then, make a well in the flour mixture and add the yeast and the small amount of sugar to the well.
Heat your seltzer water to 90 degrees Fahrenheit and pour it into the well. Let stand for five minutes so the yeast can activate, then add the vinegar and lemon juice.
Use a sturdy spatula to stir everything together. Make an indentation in the dough, then add the extracts, vegan butter, and salt. Let them sit in the indentation for now and do not stir them in yet.
Place your bowl in a clean trash bag, twist the end of the bag, and tuck the end under the bowl. This creates a proofing box in which your dough can rise in ideal conditions. Set a timer for 75 minutes.
When your timer goes off, use a hand mixer with dough hooks on high speed, or a stand mixer with the paddle attachment on medium speed to mix your dough for about 1 1/2 minutes, until all of the butter is incorporated. Use a sturdy spatula to scrape down the bowl, then knead the dough by hand in the bowl about 20 times to be sure the dough has been evenly mixed.
Put the bowl back in the plastic bag and set a timer for 30 minutes.
While you wait for the dough to rise again, draw an 18 x 12 inch rectangle on a large piece of parchment. Turn the parchment over so the side with the ink is facing the table. Spray the top of the parchment with non-stick spray, then spread the spray out evenly over the entire rectangle. This is absolutely necessary because you will not be able to get your dough to roll up properly if it is sticking to the parchment.
Prepare your pan(s) according to the directions in the blog post.
When your timer goes off, remove the bowl from the plastic bag. Use a sturdy spatula to cut into the dough and fold it about 15 times. You want to knock the air out of the dough so it is easier to shape.
Transfer your dough to the prepared parchment paper. Gently stretch and pat the dough out evenly until it fills the entire rectangle.
Follow the directions in the blog post for mixing the cinnamon filling together, and for rolling and cutting your pieces of dough. Place your dough pieces in your prepared pans.
For either size rolls, place your pan(s) in the plastic bag to rise. This will take 20 to 60 minutes, depending on the temperature and humidity. Set a timer for 20 minutes to check on them, and then recheck every 10 minutes until they are ready. Your rolls should be puffed up and there should be tiny bubbles starting to show on the top of the dough.
While you wait for your dough to rise, place a large, shallow pan of water on the lower rack of your oven, then preheat your oven to 400 degrees Fahrenheit. Check on your water level when your rolls are getting close to being ready to bake. It needs to be at least 1/4″ deep when your rolls go into the oven, so add more water if necessary.
Bake the 2 pans of smaller rolls for 29 to 31 minutes at 400 degrees and the 1 pan of larger rolls for 31 to 34 minutes.
Make the icing while the rolls are baking. Cut the vegan butter into cubes and add them to your bowl. Beat on high speed until smooth, then add the powdered sugar, vanilla, and plant milk. Beat on low speed until all of the powdered sugar is incorporated, then scrape down the bowl. Beat on high speed for about a minute, then scrape down the bowl again and set it aside for now.
Get your rack ready while the rolls are baking, and place a large piece of waxed paper under the rack. Place the pan(s) of baked rolls on the cooling rack when they are done.
Remove your baked rolls from the oven and place the pan(s) on your cooling rack. Leave the rolls in the pan for a few minutes, then move the rolls out of the pan(s) to the rack. Use a plastic knife to loosen the smaller rolls from the muffin tins, then lift each roll out and place it directly on the rack. Use the parchment paper to slide the larger rolls onto the rack while still on the paper.
For both sizes, equally divide half of the icing among the hot rolls and let it start to melt a bit. Then, use the back of a spoon to spread the icing out over the top of each roll.
Wait 10 minutes, then separate the larger rolls and place them directly on the rack. Add the remaining icing and spread it out on top of each roll. Serve immediately and enjoy!
If you want to freeze leftover rolls, place them on a plate and put them in the freezer unntil they are frozen. Then, place the rolls in a ziplock bag to store them. Reheat a roll on a plate in your microwave on 50% power until it is hot all the way through to the center. A smaller roll will take about 2 1/2 to 3 minutes, and a large roll will take about 3 1/2 to 4 minutes.