Combine the shredded mozzarella and cubed cream cheese in a large bowl. Microwave for 2 minutes, stirring halfway through. Stir again at the end until well mixed.
Stir in coconut flour and eggs into the melted cheese mixture. Knead with your hands until a dough forms. The dough will be very sticky, but just keep kneading. If the dough becomes hard before fully mixed, or is too difficult to mix, you can microwave for 15-20 seconds to soften it.
Divide the dough into 6 parts. Form a long log with each part, then press the ends together to make a bagel shape on the lined baking sheet. Repeat with the remaining dough. If using sesame seeds, sprinkle them over the bagels and gently press into the dough.
Bake for 10-14 minutes, until the bagels are firm and golden.