Prepare a half sheet pan lined with parchment paper and set aside. Preheat the oven to 400F
In a large mixing bowl, combine the flour and Greek yogurt, mix well. Then add cinnamon, brown sugar and white sugar. Knead into the dough adding more flour as needed for stickiness.
Turn onto a floured counter and knead and shape into a ball. Weigh ball and divide by 12 for 12 equal bagel-donut pieces.
Using extra flour if needed, flatten each small ball into a round disc, then add 1/2 teaspoon (or up to 1 teaspoon if you prefer more) cream cheese to center. Fold edges up around it to seal it in and gently roll into a ball again.
Place filled bagel-donuts on a sheet pan and continue with remaining dough.
Bake for approximately 15 minutes or until cooked through.
After removing from oven, allow to cool for a few minutes and during this time prepare a bowl of melted butter and separate bowl of the cinnamon sugar mixture.
Once they are cool enough to handle, dip and roll in the melted butter and then straight into the cinnamon sugar mixture.
Serve warm or cool.
Refrigerate leftovers after 1-2 hours at room temperature.