Preheat oven to 300°F (149°C). Line a large baking sheet with parchment paper.
Add egg whites to the bowl of a stand mixer. (You can also use a hand mixer but it is easier to gradually add in the honey using a stand mixer). Beat the egg whites at highest speed until they become frothy. Without turning off your mixer, gradually add in the honey and continue to beat until stiff peaks form. If your honey splatters to the sides of the bowl, you can stop your mixer to scrap the honey off the sides and add it back into the mixture. Do this before the mixture forms stiff peaks because you don't want to overbeat your egg whites.
Use a spatula to scoop out half of the batter. Place it on one side of your prepared baking sheet. Use your spatula to shape the bread into an oval. It should be about 2.5 inches tall at the highest point. Try to smooth the surface as much as possible. Repeat with the remaining mixture. Make sure to space the two bread loaves at least 2 inches apart because they will rise and expand during baking. See photo in post for reference.
Place bread into the oven and bake for about 25-30 minutes. When the loaves are done, they should be a medium brown color. When you press down on the surface lightly, it should bounce back. My bread looked ready at 25 minutes but I like to bake slightly longer to cook off the egg white flavor and add more crust. When the bread first comes out of the oven, the surface will look firm (though it won't feel firm). See photo in post for reference of how they look right after they are out of the oven. However, they will start to deflate soon after. This is normal.
Let bread cool before cutting and eating. They do stick a little to the parchment paper so you need to carefully peel them off. I don't recommend eating the bread right away because it tastes eggier when still warm from the oven. I prefer to wait a few hours. I sliced my loaves in half with a sharp bread knife.
Notes
I discuss the texture and taste of these bread loaves in detail in the post. I made several changes to the original version so they are not as eggy but the bread does have a slight eggy taste. The outside tastes like soft, chewy bread and the middle is very airy and melts in your mouth and tastes a little like eating a marshmallow.
As I discuss in the post, you can make these even smaller. They won't be as fluffy but they will taste like soft and chewy bread. My favorite variation is to divide the batter into four loaves and bake for 25 minutes. They look like fluffy pancakes but taste like soft bread.
This recipe uses standard US large eggs. I have not tried this recipe with liquid carton egg whites. I don't think they will work as well because it's harder to beat liquid carton egg whites to stiff peaks.
The bread is lightly sweetened but not super sweet. Since this is a bread I didn't want to make it too sugary. Also if you add too much honey, you won't be able to whip the mixture to stiff peaks.
The nutrition information provided are only estimates based on an online nutritional calculator. This is not a comprehensive list of all the nutrients in the recipe (i.e., does not include vitamins, cholesterol, etc). I am not a certified nutritionist. Please consult a nutritionist or doctor for accurate information and any dietary restrictions and concerns you may have.