In a mug, stir together the water, vinegar and food coloring. Place an uncooked, room temperature egg into the mug and allow it to remain in the mug for 5 minutes. Color an additional 5 eggs.
In a mixing bowl, whisk together 1/2 cup flour, the yeast and a 1/2 cup of lukewarm milk. Let it sit for 5-10 minutes or until it foams up.
On low speed, using a dough hook, slowly add the yeast mixture, 2 room temperature eggs, 1/4 cup of melted butter (cooled), 3/4 cup of room temperature sour cream, lemon zest, sugar and salt. Turn speed to medium and gradually add the remaining flour, a 1/2 cup at a time, continue mixing for 5 minutes. Add vegetable oil one tablespoon at a time add continue mixing for 10-15 minutes.
Turn dough out onto a lightly floured surface and knead by hand for 5 minutes. Place in a lightly oiled bowl, cover and leave at room temperature until it doubles in size, about 1 1/2 hours.
Divide dough into 12 equal sized balls. Using your hands shape each of the balls into a 14-inch rope. Using two of the ropes, twist them together then shape it into a ring, make sure that you pinch the ends together.
Place on a parchment lined baking sheet, place a colored egg in the center, cover with a clean dish towel or plastic wrap and allow it to rise for 30 minutes.
Place oven rack in the center of the oven and preheat to 375°F. Brush the dough with the remaining milk and top with sprinkles.
Bake for 22-25 minutes or until golden brown. Allow to cool on the pan for 5-10 minutes then transfer to a cooling rack to finish cooling. Allow to cool completely before serving.