Heat the olive oil in a deep frying pan with a heat-resistant or removable handle, add the onions and garlic, cook, stirring occasionally, for about 4 minutes, until slightly soft.
In the meantime, cut the ham into thin cubes 5 centimeters long. Set aside.
Put the zucchini and bell pepper in a pan with onions and garlic, cook everything together for about 3-4 minutes.
Add paprika, tomatoes, tomato paste, ham to a frying pan with vegetables, season with salt and pepper to taste. Bring the mass to a boil, cook the sautéed vegetables and ham over medium-low heat for about 15 minutes.
Reduce heat to low. In the total mass of vegetables and ham, make 4 indentations and pour one egg into each, salt and pepper to taste. Cook over low heat until the egg white grabs.
Switch on the oven with top grill function for preheating. Sprinkle the contents of the pan with cheese and place the pan under the grill, cook for about 5 minutes. Serve vegetable sauté with ham and eggs right away, well with country bread (optional).