Activate the yeast: Pour the warm milk into a large mixing bowl. Add the sugar, active dry yeast, and 3 tablespoons of flour. Stir until combined and let the mixture rest for 5-10 minutes, or until foamy and bubbly.
Prepare the dough: Add 4 cups of flour, salt, and softened butter to the activated yeast mixture. Mix until a soft dough begins to form.
Knead the dough: Transfer the dough to a lightly floured surface and knead for 8-10 minutes, or use a stand mixer fitted with a dough hook. The dough should become smooth, soft, and elastic. Keep it slightly tacky because more flour may be needed when the natural colors are added.
Divide the dough: Divide the dough into three equal portions. Using a kitchen scale will help ensure that each color produces 8 evenly sized buns.
Make the yellow dough: Add the turmeric to the first portion. Knead until the color is evenly distributed and the dough becomes a warm yellow shade.
Make the green dough: Add the spinach puree to the second portion. Knead until the dough is evenly green. If it becomes sticky, add extra flour one tablespoon at a time until it is soft and manageable.
Make the pink dough: Add the cooked beet puree to the third portion. Knead until the dough is evenly pink. Add extra flour one tablespoon at a time if necessary, but keep the dough soft.
Complete the first rise: Place each colored dough portion in a separate lightly greased bowl. Cover with plastic wrap or clean kitchen towels. Let the dough rise in a warm, draft-free place for approximately 1 hour, or until doubled in size.
Shape the buns: Divide each colored dough portion into 8 equal pieces, creating 24 pieces in total. Shape each piece into a smooth, round ball by tucking the edges underneath.
Complete the second rise: Arrange the buns on baking sheets lined with parchment paper, leaving space between them. Cover loosely and let them rise for 20-30 minutes, or until soft and puffy.
Brush and add the topping: Preheat the oven to 350°F (180°C). Mix the water and oil in a small bowl. Gently brush the risen buns with the mixture and sprinkle with sesame seeds, if desired. Reserve the remaining mixture for brushing after baking.
Bake: Bake the Colored Burger Buns for 20–25 minutes, or until baked through and lightly golden. Avoid overbaking, as this can dry out the buns and darken their natural colors.
Brush after baking: As soon as the buns come out of the oven, gently brush them with the remaining water-and-oil mixture. This helps keep the crust soft and adds a light shine.
Cool: Transfer the buns to a wire rack and allow them to cool before slicing and serving.