In a large bowl, combine the softened butter, oil, yogurt, 1 whole egg plus 1 egg white (reserve the yolk), salt, sugar, and baking powder. Gradually add the flour and mix until a soft, smooth dough forms.
Fold in the chopped dill, parsley, grated carrots, and a pinch of red pepper until evenly distributed.
Divide the dough into pieces of about 80g each (roughly 20 pieces).
Flatten each piece by hand into a small disc, place a spoonful of cheese in the center, then fold and seal the dough around the filling.
Arrange the shaped buns on a parchment-lined baking tray, spaced slightly apart.
Beat the reserved egg yolk and brush over the top of each bun.
Bake in a preheated oven at 180°C (356°F) for 20–25 minutes, until golden brown.
Let rest a few minutes before serving warm.
Notes
Store cooled buns in an airtight container at room temperature for up to 2 days, in the fridge for up to 4 days, or freeze (baked or unbaked) for up to 2 months.