Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large mixing bowl, whisk together the eggs, milk, salt, black pepper, garlic powder, and mustard powder until well combined.
In a skillet over medium heat, add the olive oil. Sauté the diced onion and bell pepper for about 3-4 minutes until softened. Add the chopped spinach and cook for an additional 2 minutes. Remove from heat.
Stir the sautéed vegetables, diced ham, and half of the shredded cheddar cheese into the egg mixture. Mix until evenly distributed.
Pour the egg mixture into the prepared baking dish. Sprinkle the remaining cheddar cheese on top.
Bake in the preheated oven for 30-35 minutes, or until the casserole is set and the top is golden brown. A toothpick inserted in the center should come out clean.
Allow the casserole to cool for 5-10 minutes before slicing and serving.