Peel the tomatoes: If using fresh tomatoes, warm the butter and 1 tablespoon olive oil in a medium skillet over medium heat. Add tomatoes, cut side down, and cover. Cook until the tomato skins begin to wrinkle and, when pinched, you can easily slide them off, about 4 minutes. Transfer the tomatoes to a plate to cool. Once cool, pinch the skins off the tomatoes and discard. If using canned tomatoes, you can skip this step.
Sauté the vegetables: Add the onion, bell pepper, and a pinch of kosher salt to the medium skillet where the tomatoes were cooked. Cook, covered, stirring occasionally, until completely soft and nicely golden, about 6 minutes. Add garlic and cook 1 minute more until fragrant. Meanwhile, finely chop the tomatoes.
Bloom the Piment d'Ville: Push the vegetables to the edges of the pan and add 1 remaining tablespoon of olive oil. Add Piment d'Ville and ground cumin and let them sizzle in the oil for about 30 seconds, stirring. Then stir everything together so the spices coat the vegetables.
Build the tomato sauce: Add tomatoes and another pinch of salt. Raise the heat to medium-high and cook, stirring occasionally and breaking up the tomatoes with a spoon, until the sauce thickens and most of the liquid has cooked off.
Add the eggs: Crack 4 eggs into a bowl and stir briefly, just enough to break up the yolks and make a streaky mixture. Reduce the heat to medium-low and pour the eggs into the pan. Using a wooden spoon or heat-proof spatula, gently and slowly fold and stir the eggs into the sauce, pulling the set edges inward and letting the loose egg flow out to the sides. Stop when the eggs are just barely set and still look glossy and a little underdone, they'll finish cooking from residual heat of the pan. This should take about 3 minutes and the mixture will look varied, not uniform: red tomato sauce, with white and yellow streaks of cooked egg.
Finish and serve: Remove from heat immediately. Dust with an extra pinch of Piment d'Ville, crumbled feta cheese, and parsley. Bring the whole skillet to the table and serve with plenty of crusty bread or warm flatbread, for serving for swiping up every last bit of sauce.
