Start by preparing the dough. In a bowl, whisk mayo, oil, salt, water, and milk. Sprinkle yeast over the mixture, and then add sugar over the yeast. Cover the bowl with a kitchen towel and let it sit for 5 minutes to allow the yeast to activate and become foamy.
Gradually incorporate the flour into the mixture, ensuring it is well combined. Set the dough aside to rise at room temperature, covered, for 1 ½ to 2 hours, or until it doubles, almost tripling in size.
Preparing the Filling:
In a large skillet over medium-high heat, cook the chicken in 1 tsp of oil until fully cooked (approximately 2-3 minutes), stirring as needed. Remove it from the skillet.
Sauté the onion in 1 Tbsp of butter until it’s tender, stirring frequently. Add the remaining 2 Tbsp of butter, cabbage, carrots, garlic, and water. Season with salt and pepper, and sauté until the cabbage reaches your desired level of tenderness.
Add the ketchup, sour cream, herbs, and the cooked chicken. Cook for another minute, stirring frequently. Remove from heat and let it cool.
Assembling the Pirog:
On a lightly floured surface, divide the dough into 2 equal parts (cover the second piece of dough). Roll it out until it’s approximately 12” round.
Take half of the cabbage filling and place it in the center of the dough, spreading it evenly (leaving about 3” of dough uncovered around the edges).
Gently fold the edges of the dough over the filling, bringing them into the center to close the pirog. Continue all the way around until the cabbage is completely covered. Pinch the seams together.
Carefully flip the pirog over and flatten it as needed to ensure an even size and an even distribution of the filling. Repeat the process with the second pirog.
Brush with an egg wash, sprinkle with sesame seeds (if desired), and let it rise for 30-45 minutes.
Bake in a preheated oven at 400°F for 18-22 minutes, or until the pirog achieves a golden hue.
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