Lightly grease a medium bowl with peanut or vegetable oil; set aside. Pour ⅓ cup lukewarm water into a small bowl, sprinkle 2 tsp. instant dry yeast over, and let sit 1 minute to soften yeast. Add ½ cup lukewarm whole milk or oat milk, 3 Tbsp. sugar, and 2 Tbsp. peanut or vegetable oil and stir until yeast and sugar are dissolved.
Mix 1½ tsp. baking powder and 2½ cups plus 5 Tbsp. plus 2 tsp. (355 g) all-purpose flour in the bowl of a stand mixer to combine. Make a well in the center and pour in yeast mixture. Stir with a rubber spatula to form a ragged dough that mostly cleans the sides of the bowl as you mix it. Let sit, uncovered, 3 minutes.
Attach bowl to stand mixer fitted with dough hook and beat on medium speed until dough forms a ball around hook, about 1 minute. Continue to beat until dough is mostly smooth and elastic but still sticky, about 30 seconds.
Using a flexible dough scraper, transfer dough to a lightly floured surface and turn to coat dough lightly in flour to make it easier to handle. Gently knead until smooth, soft, slightly tacky, and roundish in shape, about 30 seconds. When you press a finger into the dough, it should spring back, leaving only a faint indentation. (Alternatively, you can mix the dough in a large bowl with a rubber spatula and some elbow grease. Knead on a surface, dusting lightly with flour, until a soft, smooth dough forms, about 4 minutes. If the dough feels work in water by the teaspoonful as needed.)