Prep Your Ingredients: Before you begin, get all your ingredients ready. Peel the potatoes, slice them in half lengthwise, and then cut them into uniform ¼-inch thick slices. This ensures they cook evenly. Finely chop the onion and parsley, and mince the garlic. For the peppers, slice them lengthwise, remove the seeds, and then slice them thinly.
Cook the Potatoes: In a large nonstick skillet, heat the olive oil and butter over medium-high heat. Once the butter is melted and sizzling, arrange the potato slices in a single layer. Cook for about 6-8 minutes, flipping them occasionally, until they are golden brown on both sides. Don't overcrowd the pan; cook in batches if needed. Remove the potatoes from the skillet and set them aside.
Sauté Peppers and Brown the Beef: In the same skillet, add the sliced peppers and sauté for about 3 minutes until they start to soften. Add the ground beef and use a spatula to break it into small pieces. Cook until it is lightly browned, about 2-3 minutes.
Build the Flavor: Stir in the minced garlic and chopped onion, and cook for another 2 minutes until they are fragrant and the onion is translucent. Now, add the seasonings: salt, black pepper, chili flakes, sweet paprika, and Italian seasoning. Stir well to combine. Add the tomato paste and cook for one minute more, stirring constantly to coat everything.
Combine and Simmer: Gently return the cooked potatoes to the skillet along with the chopped parsley. Stir carefully to combine without breaking the potato slices. Pour in the chicken broth, bring the mixture to a simmer, then cover the skillet with a lid and reduce the heat to medium-low. Let it simmer for about 10 minutes, or until the potatoes are fork-tender and most of the broth has been absorbed.
Melt the Cheese: Remove the lid and sprinkle the grated cheddar cheese evenly over the top. Cover the skillet again and let it cook for another 2 minutes, or until the cheese is completely melted and bubbly.
Garnish and Serve: Garnish with additional fresh parsley and chili flakes, if desired. Serve hot directly from the skillet.