1. Adjust oven rack to middle position and heat oven to 400 degrees. Pulse tomatoes and their juice in food processor until coarsely ground, about 10 pulses.
2. Heat 12-inch cast-iron skillet over medium heat for 3 minutes. Add oil and heat until shimmering. Add onion and ½ teaspoon salt and cook until softened and lightly browned, 5 to 7 minutes.
3. Stir in garlic and pepper flakes and cook until fragrant, about 30 seconds.
4. Add sausage and cook, breaking up meat with wooden spoon, until no longer pink, about 5 minutes. Stir in processed tomatoes, bring to simmer, and cook until sauce is slightly thickened, about 10 minutes; transfer to bowl.
5. In separate bowl, combine ricotta, egg yolk, thyme, 1 teaspoon salt, and ½ teaspoon pepper.
6. Combine mozzarella and parmesan in third bowl.
7. Spread 3/4 cup sauce over bottom of now-empty skillet. Shingle 7 noodle halves around edge of skillet and place 1 noodle half in center. Dollop one-third of ricotta mixture over noodles, then top with one-quarter of mozzarella mixture and one-third of remaining sauce (in that order).
8. Repeat layering process twice, beginning with noodles and ending with sauce. Top with remaining mozzarella mixture.
9. Transfer skillet to oven and bake until cheese is golden brown and lasagna is bubbling around edges, 30 to 40 minutes.
10. Let lasagna cool for 10 minutes, then sprinkle with basil and serve.