In a small bowl, whisk together the eggs, almond flour, psyllium husk powder, baking powder, and softened butter until a thick, smooth batter forms.
Pour the batter into a greased, microwave-safe square container (about 4x4 inches) and microwave on high for 90 seconds. The 'bun' will be firm to the touch.
Carefully remove the hot container from the microwave and let the bun cool for a minute before turning it out onto a cutting board.
Slice it in half horizontally to create two 'bread' slices.
Layer the cheddar cheese between the slices to assemble your sandwich.
Melt the remaining tablespoon of butter in a non-stick skillet over medium heat.
Place the sandwich in the pan and fry for 2-3 minutes per side, until the bread is golden brown and crispy, and the cheese is perfectly melted and gooey.
Serve immediately.