Step 1In a 2-quart heavy-bottom saucepan, heat the oil over medium-high heat just until it begins to ripple, about 2 minutes. Stir in the onions and garlic and cook, stirring frequently until the onions are translucent. Stir in the basil, tomatoes, salt and pepper and continue to cook, stirring frequently, until the tomatoes break down and the sauce just coats the back of a spoon, about 20 minutes. Remove from heat. This makes about 2 cups sauce.
Step 1Grill the eggplant: Brush the eggplant slices with 1 tablespoon olive oil, then season with one-fourth teaspoon salt and the pepper. Grill the eggplant on both sides to mark, then cool completely. Dice the eggplant into one-half-inch pieces.
Step 2Heat the remaining oil in a large saute pan over medium-high heat until it begins to ripple. Stir in the onions and garlic and cook, stirring frequently, until the onions are translucent. Stir in the herbs and tomato sauce and bring to a boil. Fold in the eggplant with the crushed red pepper, roasted red pepper, red wine vinegar and remaining teaspoon salt. Remove from heat, taste and adjust seasonings and flavoring as desired.
Step 1Heat the oil in a 2-quart saucepan over medium-high heat until it begins to ripple. Stir in the lamb and brown, stirring frequently. Add the wine and scrape any flavoring from the bottom of the pan. Cook until the wine is reduced by half. Stir in the demi-glace and reduce the total liquid by one-third. Stir in the tomato sauce, fresh mint and simmer for 20 minutes. Remove from heat and season to taste with salt and pepper. This makes a generous 2 cups of the sauce.
Step 1Roast the tomatoes: Heat the oven to 375 degrees. Slice the tomatoes lengthwise into slices approximately one-fourth-inch thick and place on a parchment-lined baking sheet. Sprinkle over 2 tablespoons oil, and season with a generous pinch each of salt and pepper. Roast the tomatoes until lightly caramelized on top but still somewhat soft in the center, 10 to 15 minutes. Remove from heat.
Step 2Cook the pasta: Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, 8 to 10 minutes. Drain the pasta and toss with 2 tablespoons olive oil. Spread the pasta on a baking sheet to cool slightly. The pasta can be made up to this point and all of the components refrigerated for up to 2 days before completing the dish.
Step 3Heat the remaining one-fourth cup oil in a medium heavy-bottom pot over medium-low heat until it begins to ripple. Add the shallots and cook, stirring frequently, until lightly browned, about 1 minute. Stir in the cooked pasta, then stir in 1 1/2 cups of lamb sauce. Gently stir in the eggplant caponata. Stir in the Grana Padano and vinegar, and season to taste with salt and pepper. Remove from heat.
Step 4Spoon the pasta into large serving bowls, and spoon over the remaining lamb sauce. Sprinkle the goat cheese crumbles over the servings then sprinkle over the chopped parsley. Fan roasted tomato slices over each to garnish, and serve immediately.