Brown the meat: Heat the oil in your skillet over medium-high heat. Add the ground beef and cook, breaking it up, until it is deeply browned and crisp in spots — about 6 to 7 minutes. Don't stir it constantly. Let it sit so the Maillard reaction can do its thing. Use a slotted spoon to transfer the meat to a bowl, leaving the fat behind.
Sauté the aromatics: Lower the heat to medium. Add the onion and cook until soft, about 4 minutes. Add the garlic and cook for 30 seconds until fragrant.
Bloom the paste: Push the onions to the side, add the tomato paste directly to the pan, and stir it in the hot fat for about 2 minutes. It will darken and smell almost sweet. Add the oregano and red pepper flakes and stir.
Deglaze and build the sauce: Pour in the stock and scrape up all the browned bits from the bottom with your spoon. Add the crushed tomatoes, 1/2 teaspoon of salt, and several cracks of black pepper. Bring it to a simmer.
Cook the pasta: Stir in the broken lasagna noodles, pressing them down so they are fully submerged in the sauce. Return the browned meat to the pan. Cover, reduce the heat to low, and simmer for 18 to 22 minutes, stirring once halfway through, until the noodles are tender. If it starts looking dry before the pasta is done, add a splash of warm water or stock.
Prepare the ricotta: While the pasta cooks, stir together the ricotta, egg, the 1/2 cup of Parmesan, and a pinch of salt.
Add the cheese: Dollop the ricotta mixture evenly over the top of the cooked lasagna. Sprinkle with the shredded mozzarella. Cover again and cook on low for 5 minutes, then remove the lid and let it sit for 2 to 3 minutes so the top sets.
Rest and serve: This is the hardest step: let the skillet sit off the heat for 5 full minutes. The lasagna will firm up as it rests and the sauce will tighten. Top with torn fresh basil and serve hot.