1. To make the hash, melt the butter and oil in a 10-inch cast-iron skillet over medium-high heat (a large non-stick skillet is fine if you don’t have one). Add onions and peppers and cook for 5 minutes, or until the vegetables begin to soften. Add the potatoes and cook, turning occasionally for 15 to 20 minutes, or until the potatoes are cooked through. Season with salt and pepper. Add the garlic and cook for an additional minute. Remove from heat and stir in parsley and thyme.
2. To fry the eggs, heat a non-stick sauté pan over medium heat. Melt butter in the bottom of the pan and swirl to coat. Crack the egg into the pan. (I like to use a small glass or measuring cup to crack the egg and then pour it into the pan.) Cook until the whites are cooked, and the yolks cook to your preference. If you prefer a more cooked yolk, add a tablespoon of water to the pan and cover for a minute or two.
3. Serve the eggs over top of the hash and season well with salt and pepper.
To cut down on cook time, use small potatoes and cut them into circles instead of quarters. You get a nice crust on the outside and the inside is tender and fluffy, without having to steam them first. Topped with fried eggs, this is a complete meal that everyone will love.