In a glass measuring cup, combine the water, yeast, and sugar; set aside to foam for about 5 minutes. In the bowl of an electric mixer fitted with the whisk attachment, beat the pudding mix and milk together until combined and thickened. Add the butter, Greek yogurt, egg, salt, and food coloring, beating until fully combined.
Switch to the dough hook, and add the yeast mixture and 3 cups of the flour. Mix the dough on low and allow it to knead for about 6-7 minutes. If dough is still too soft, add more flour, 1 Tablespoon at a time, until dough just cleans the bowl, but is very soft. It should still stick to the bottom of the bowl.
Coat a large bowl with cooking spray and place dough in bowl. Seal tightly with plastic wrap. Place bowl in a warm place and allow dough to rise until doubled in size, about 2 hours. In the meantime, spray a 9-by-13-inch pan with nonstick cooking spray; set aside.
After dough has doubled in size, punch it down. Turn dough out onto a floured Silpat or floured countertop. With a rolling pin, roll it out to a 16-by-12-inch rectangle.
With a knife (or your fingers), spread butter evenly over the entire surface of the dough. Sprinkle the brown sugar over it, followed by the cinnamon and cocoa powder. Lightly pat it down with your fingertips to help sugar adhere to dough. Roll dough tightly into a log, ending with the seam side down. Pinch the ends to seal.
Using plain, unwaxed dental floss (or a bench scraper), slice the rolls into 12 evenly-sized rolls. Arrange the rolls cut side down in the prepared baking pan. Cover tightly with plastic wrap.