In a large bowl, whisk together 3 ½ cups flour, yeast, sugar, and salt.
Then, add in the water.
Using a spatula, fold until mostly combined. Sprinkle a little more flour if needed to not be sticky and form a ball.
Once ball is formed, grease the same bowl mixed in and place the dough ball back into the bowl. *If you are oil free, then just make sure sides of bowl are floured, or use a silicone bowl to easily get it out Cover with a towel or plastic wrap and let sit for 60-90 minutes in a warm, draft free place until doubled.
Once doubled in size, pull out the dough and lay it out on a lightly floured surface.
Using a rolling pin, roll dough into an approximately 18×12″ rectangle.
Beat together ¼ cup softened butter and the cream cheese. Fold in 1 cup vegan mozzarella cheese. Spread across the dough.
Sprinkle the vegan ham across the dough, then the broccoli, then the remaining mozzarella cheese.
Carefully roll into log from the longest side up. One completely rolled, place seam side down. Cut into 12 even sized pieces. *It's okay if some of the sauce comes out, but try to tuck and roll as you go along. Place into a greased baking dish and cover. Let rise for an additional 45-60 minutes.
Preheat over to 375 degrees F.
Right before going into the oven, brush the tops with the remaining vegan butter.
Once heated, place dish inside and bake in oven for 35-45 minutes or until dough is cooked inside.
Remove rolls from oven when done. Let cool for 5-10 minutes before serving.
Store any leftovers in an air tight container.