Peel and devein the shrimp and then cut in half lengthwise. In a large bowl, combine the shrimp, 1 Tbs. of the oil, 1/2 tsp. of the garlic, the lemon zest, 1/2 tsp. salt, and 1/4 tsp. pepper and toss to mix well. Cover and refrigerate for at least 30 minutes and up to 8 hours.
Prepare a hot gas or charcoal grill fire. Cut the tops and bottoms from the peppers and cut the peppers into 3 or 4 flat pieces, discarding the tops, seeds, and ribs. Grill the pepper sides and bottoms skin side down until blistered and charred all over, 6 to 8 minutes. Put the peppers in a bowl and cover with a plate. Let sit until cool enough to handle. Peel the charred skin and discard. Don't be too concerned if flecks of skin remain attached. Cut the peppers into thin strips.
Heat 1-1/2 Tbs. of the olive oil in a 12-inch skillet over medium heat. Add the breadcrumbs and the remaining 1/2 tsp. of garlic, and stir frequently until the smaller crumbs are golden brown and crisp, 3 to 4 minutes. Remove from the heat, season with salt and pepper, and transfer to a small bowl. Carefully wipe out the pan with a paper towel.
Bring a large pot of well-salted water to a boil over high heat. Cook the fettuccine in the boiling water, stirring frequently at first, until al dente, about 11 minutes.
While the pasta is cooking, heat 1 Tbs. of the olive oil in the skillet over medium-high heat. Add the shrimp and cook, stirring frequently, until curled and turning opaque, about 1 minute. Add the peppers and shallot and season with 1/2 tsp. each salt and pepper. Continue to cook, stirring, until the shrimp are mostly opaque, about 1 minute more. Ladle 1/4 cup of the boiling pasta water into the skillet and cook until the shrimp are cooked through, about 1 more minute (be careful not to overcook).
Reserve another 1/4 cup of the cooking water and drain the pasta. Return the pasta to the pot and add the shrimp mixture, the remaining 1 Tbs. olive oil, the arugula, and the basil. Toss well and season to taste with more salt and pepper. If the pasta looks dry, add some of the reserved pasta water. Divide among 4 warm serving bowls and sprinkle with the toasted breadcrumbs.