Preheat your oven to 350ºF. Line an 8-inch round baking pan with parchment paper to prevent the rolls from sticking and to make removal easier later.
In a large microwave-safe bowl, combine the shredded cheddar or mozzarella cheese and butter. Microwave on high in 30 second intervals, stirring after each, until the cheese and butter are melted and can be stirred together into an almost liquid mixture. This helps the dough come together smoothly in the next step.
To the melted cheese and butter mixture from Step 2, add the coconut flour, plain whey or egg white protein powder, baking powder, garlic powder, and salt. Stir to partially combine, then add the eggs and egg white. Use a rubber spatula to mix and knead until the dough becomes uniform and cohesive. The dough will be quite sticky.
Lightly oil your hands (to prevent sticking), then divide the dough (from Step 3) into 8 equal portions. Roll each portion into a ball and place them evenly spaced in the prepared baking pan from Step 1.
In a small bowl, whisk together the melted butter, minced garlic, chopped parsley, and coarse salt to make the garlic butter. Brush about half of this mixture generously over the tops of the dough balls in the pan. I like to use extra parsley here for a pop of color and freshness.
Bake the rolls in the preheated oven for 20 to 25 minutes, or until they are puffed, golden brown, and firm to the touch. Remove from the oven and let cool in the pan for about 15 minutes before removing and breaking apart. Once cooled slightly, brush with the remaining garlic butter from Step 5 and serve warm.