1. Whisk together 3 1/2 cups flour, yeast, sugar, water, and salt and add to a Kitchen-Aid mixing bowl.
2. Using a dough hook attachment, blend for 6-8 minutes on low until the dough forms into a ball.
3. Once the ball is formed, remove it, and grease the same bowl it was mixed in. Place the dough ball back into the bowl. *If you are oil-free, then just make sure the sides of the bowl are floured, or use a silicone bowl to easily get the dough out.
4. Cover with a towel or plastic wrap, and let sit for 60-90 minutes in a warm, draft-free place until doubled.
5. While the dough is rising, make the pesto by adding everything from the filling into a blender or food processor.
6. Blend, scraping down as needed until well combined.
7. Once doubled in size, pull out the dough, and lay it out on a lightly floured surface.
8. Using a rolling pin, roll dough into an approximate 18×12″ rectangle.
9. Spread the pesto evenly across the dough. Sprinkle the chopped parsley evenly across the dough.
10. Carefully roll into a log by starting with the longest side. Once completely rolled up, place seam side down. Cut into twelve even-sized pieces. *It’s okay if some of the filling comes out, but try to tuck and roll as you go along.
11. Place in a greased pan or cast iron pan.
12. Preheat oven to 375 degrees F.
13. Once heated, place dish inside and bake in oven for 30-35 minutes or until dough is cooked inside.
14. Make the vegan butter topping by melting vegan butter and adding salt and parsley. Remove rolls from oven when done, and brush with this buttery mix. Enjoy!
15. Store any leftovers in an air-tight container.