Preheat the oven to 300 degrees F. Grease 2 baking sheets very well or line with parchment paper. (I actually find these work best cooked on parchment that has been lightly oiled or sprayed.)
Separate the eggs*, placing the whites in a large mixing bowl or the bowl of a stand mixer and the yolks in a small bowl. Make sure no yolk mixes in with the whites.
Add the softened cream cheese and honey to the egg yolks, and whisk with a fork until very smooth. A few little pieces of visible cream cheese is okay.
Start beating the egg whites on low speed. When the whites become frothy, add the cream of tartar. Resume beating, slowly increasing the speed to medium-high for a stand mixer or high for a handheld mixer. Stop beating and check occasionally, and then stop beating when the egg whites form stiff peaks. (If the eggs droop over when the beater is lifted, you’re at the soft peak stage. Beat just until the whites stand up straight without slumping. Beating beyond this stage will cause the whites to become dry and separate; stopping at the soft peak stage will result in a batter that’s too runny.)
Very carefully fold the egg yolk mixture into the egg whites until combined. Proper folding will prevent the fluffy egg white mixture from breaking down too much.
Using a large spoon, scoop 8 to 10 similar size rounds onto the prepared baking sheets. The rounds should be roughly 3/4-inch thick and 4 to 5 inches across. Adjust them gently with the spoon. You can make different shapes (like oblong), if preferred. Just try to keep the size and thickness consistent.
Bake on the middle rack for approximately 25 to 30 minutes. (If you can’t fit your baking sheets on the same rack, rotate them midway through the cooking time.) Cooking times will vary based on oven, so be sure to watch closely. The tops should be golden brown and the buns should not feel mushy when lightly pressed in the center.
Once cooked, cool completely. Store in a single layer in a zip-top bag or airtight container in the refrigerator overnight. (If stacked, the rolls will stick to each other.) As the bread rests, the texture will improve and the egg flavor will lessen. I find that the flatter side–the side that was touching the baking sheet–works better as the part of the roll your hands touch when using as a sandwich roll.
