Preheat your oven to 350°F and lightly grease a 9x13 inch baking dish with butter or cooking spray. While the oven heats, dice the green pepper and onion into bite-sized pieces, cube the ham into 1/2-inch pieces, and mince the garlic cloves. Having everything prepped and ready will make assembly quick and seamless.

Crack all 8 eggs into a large bowl and whisk them together until the yolks and whites are fully combined. Add the Greek yogurt, salt, black pepper, and smoked paprika if using, and whisk until smooth and well incorporated. The yogurt will create a creamy, custardy texture in the final bake. I like using Fage 5% yogurt here because it's thick enough to add richness without making the eggs watery.

Scatter the diced peppers, onion, ham, and minced garlic into the prepared baking dish, distributing them evenly across the bottom. Pour the egg and yogurt mixture from Step 2 over the vegetables and meat, stirring gently to distribute everything evenly. Sprinkle 1 cup of the cheddar cheese over the top, reserving 1/4 cup for the final layer. For the best cheese pull and even melting, I like using sharp cheddar like Tillamook because it adds great flavor without being too overpowering.

Place the baking dish in the preheated 350°F oven and bake for 30 minutes. The eggs should be mostly set around the edges but still slightly jiggly in the center when gently shaken—this is exactly where you want them at this point.

Remove the baking dish from the oven and sprinkle the reserved 1/4 cup of cheddar cheese evenly over the top. Return to the oven and bake for another 10 minutes, until the cheese is melted and the center of the egg bake is fully set but still moist. The eggs should not jiggle when you gently shake the pan.

Remove the baking dish from the oven and let it rest for 5 minutes before cutting into portions. This brief rest allows the eggs to firm up slightly and makes serving easier. Cut into squares and serve warm.