In a large mixing bowl or the bowl of your stand mixer fitted with a hook attachment, combine the active dry yeast and warm water. Stir it around and let sit for 5 minutes until the mixture is foamy.
Add bread flour, oat flour, sugar, and salt. Mix by hand or with the dough hook at low speed for 1 minute. Once all of the ingredients are mixed, add olive oil and slowly knead by hand or with your dough hook on low-medium speed until all is combined. After kneading, your dough should be smooth and elastic.
Shape the dough into a ball. Cover tightly with plastic wrap and allow to rise in a warm environment (about 75°F or 80°F/24°C or 27°C)* for 1 hour or until doubled in size.
While the dough is rising, prepare a cream cheese mixture. Put cream cheese and feta cheese in a small bowl and mix until combined. Set it aside in the refrigerator.
Once the dough has risen, punch the dough down to release the air. Divide the dough into 30g each (or about the size of a ping pong ball). Flatten each piece with your fingers or use a rolling pin. Place the cream cheese mixture in the center of the flattened dough, then fold the dough around to wrap the filling inside. Pinch the opening to seal as best as you can. Repeat this process until you have 14 bagel bites and set them aside in a warm environment.
Preheat the oven to 400F.
In a large pot, start heating up some water. Once the water starts boiling, drop the bagel bites and boil them for about 1 minute. Then take them out of the water and drain.
In a small bowl, place Everything bagel seasoning. Roll the bagel bites in the seasoning to coat them all around then place them on a baking sheet lined with parchment paper.
Bake the bagel bites for 10 minutes or until the tops are golden brown. Remove the bagel bites from the oven and allow them to cool.