Use a tablespoon, or small cookie scoop, to place dollops of cream cheese onto a parchment paper, or foil lined sheet pan. Place into the freezer to harden while you make your dough.
In a large bowl combine self rising flour with Greek yogurt until you have a shaggy, clumpy dough. If the dough seems too dry, add more yogurt, one tablespoon at a time, up to ¼ cup, until it comes together.
Dump the dough onto a lightly floured counter. Gather together into a rough ball and knead the dough for 3 to 4 minutes, or until you have a soft dough with a smooth surface. Dust the counter with more flour if the dough sticks (see pictures in post, above).
When done, the dough should be smooth and only a little bit sticky. Shape into a ball and cover with plastic wrap. Let rest for 15 minutes, while you preheat the oven to 375°F.
Divide into 12 equal pieces (about 70 to 75 grams each). Shape each piece into a ball.
Flatten a piece of the dough and place a piece of frozen cream cheese into the center.
Bring all of the edges over the cream cheese ball and pinch closed. Roll on the counter, seam side down, to help seal the dough closed completely.
Make an egg wash with a large egg whisked with 1 tablespoon of water, some milk, or mix more greek yogurt with a bit of water to make a milk consistency. Brush the top of each bagel with your chosen wash. Sprinkle with your choice of topping.
Bake at 375°F for 20 to 25 minutes, or until fluffy and fully browned. Check at 20 minutes, and keep checking every minute or so to catch if any of your bagel bites start to leak. Pull out of the oven and let cool.