Place a grill pan over medium-high heat or pre-heat a gas or charcoal grill. Using a pastry brush, lightly brush the eggplant slices with 1/3 cup olive oil and sprinkle with salt and pepper. Grill the eggplant until tender and colored with grill marks, about 4 minutes per side. Set aside.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain pasta.
Meanwhile, warm the 2 tablespoons of olive oil in a large skillet. Add the onion and saute until tender, about 3 minutes. Add the beef and pork, and brown the meat, breaking it into bite-sized pieces with a wooden spoon, about 5 minutes. Add the Marsala and cook until the liquid has evaporated, about 3 minutes. Turn off the heat. Add the peas and marinara sauce and stir to combine. Add the cheeses, basil, and cooked pasta. Set aside.
Preheat the oven to 350 degrees F. Line the springform pan with the grilled eggplant. Be sure that the slices overlap and hang over the edge of the pan. Fill the pan with the pasta mixture, pressing down to make sure the pan is filling up evenly. Fold the eggplant slices up over the top of the pasta and add a few more slices on top to completely enclose the timbale. Bake the timbale until warmed through and the cheese has melted, about 30 minutes. Let rest on the counter for 10 minutes to set.
To serve, invert the timbale onto a serving plate and remove the springform pan. Sprinkle the remaining 1/4 cup grated Pecorino Romano cheese over the top. Slice and serve.