Dissolve the yeast, sugar and 110°F warm water together. Allow to proof for 10 minutes.
Meanwhile, heat the milk in the microwave for 90 seconds. Add the cold butter to cool it slightly.
Combine the 2 beaten eggs with ¼ cup oil, ½ teaspoon salt, ½ cup warm water, and 1 Tablespoon sugar.
Add the yeast mixture to the liquid.
Combine 2 cups of flour using a stand mixer with a paddle attachment.
Switch to a dough hook and add the remaining 2 cups of flour. If the dough does not pull away from the sides of the bowl, gradually add flour until it forms a ball.
Transfer the dough to a sheet of parchment paper. insert the steam rack into the Instant Pot and place the dough on top. Cover with a glass lid.
Set the Instant Pot to the Yogurt setting (not boil) for 1 hour.
Pull walnut-sized pieces of dough out of the pot and allow to rest on a board.
Flatten the dough into a circle and fill with your choice of filling.
Seal the edges and place on a cookie sheet seal side down.
Cover the pyrizhky with a tea towel and let rise 30 to 45 more minutes.
Bake in a 350°F oven for 18 to 20 minutes until golden brown.