Preheat the oven to 400°F and line a baking sheet with parchment paper.
Whisk the eggs, cottage cheese, salt and pepper. Melt the butter in a nonstick skillet over medium-low heat and cook the eggs, stirring gently, until soft and just barely set. Let them cool for 10 minutes, then stir in the ham, cheddar and chives.
Blend the cottage cheese for the dough until smooth. In a large bowl, whisk the flour, baking powder and salt, then stir in the blended cottage cheese until a shaggy dough forms.Turn the dough out onto a floured surface and knead for about 1 minute until smooth and only slightly tacky.
Divide the dough into 6 pieces and roll each into a 6-inch circle.
Spoon the filling onto one half of each circle, fold the dough over and press the edges together with a fork to seal. Place on the baking sheet, brush with beaten egg and cut a small slit in the top of each pocket.
Bake for 20 to 22 minutes, until puffed and deep golden. Let them cool for 5 minutes before serving.