Position a rack in the upper third of the oven and preheat to 350 degrees F. Whisk the half-and-half, cayenne, 1/2 teaspoon salt, and black pepper to taste in a small bowl.
Heat the olive oil in a large ovenproof skillet over medium-high heat. Add the shallots and cook until just softened, 1 to 2 minutes. Add the bell peppers; cook until the peppers are soft and the shallots are golden, 5 to 6 more minutes. Add the tomatoes, ham, bread, parsley and 1/4 cup water and cook until most of the liquid is absorbed, about 3 minutes. Season with salt and black pepper. Remove from the heat.
Make 8 evenly spaced indentations in the bread mixture with the bottom of a ladle or small measuring cup. Crack an egg into each indentation. Slowly pour the half-and-half mixture over the eggs. Bake, rotating the skillet a few times, until the whites are set, about 15 minutes. Top with parsley.