Step 1Heat the olive oil in a large skillet over medium heat. Add the garlic and saute until aromatic, 2 to 3 minutes. Finely crush the tomatoes with your hands and add to the pan along with the puree. Stir in the tomato paste, anchovies and hot red pepper flakes. Season with salt and pepper to taste. Cook, stirring often, 20 minutes.
Step 2While the sauce cooks, bring a large pot of liberally salted water to a rolling boil. Add the tagliatelle and cook according to package directions until not quite al dente. Drain well and turn into a large bowl. Toss with 2 tablespoons of the butter to keep the noodles from sticking together.
Step 3Add the tomato sauce, olives and one-half cup Parmigiano-Reggiano to the pasta and mix well to distribute all the ingredients evenly. Set aside until cooled.
Step 4Heat the oven to 350 degrees. Use the remaining butter to thickly grease a 9-inch springform pan. Dust with the panko, turning to coat the bottom and sides of the pan, shaking off the excess.
Step 5Add the mozzarella to the tagliatelle and again mix very well to distribute the cheese. Scrape the pasta into the prepared pan, pressing to compact it and smoothing the top. Sprinkle with the remaining Parmigiano-Reggiano.
Step 6Bake 45 minutes. Let stand 10 minutes. Run a thin spatula around the inside of the rim of the pan to loosen, then remove the spring form. (If any noodles pop out, just gently press them back into the timballo.) Using a very sharp knife, cut into wedges to serve.