Traditional sesame shrimp are usually deep-fried; these are broiled with vegetables and tossed with pasta. Put the water on to boil before you prepare all the ingredients, then cook the shrimp and vegetables at the same time as the pasta.
In a medium pot of boiling salted water, cook spaghetti until al dente, according to package instructions. Drain; return to pot.
Meanwhile, in a medium bowl, whisk together marmalade, soy sauce, oil, vinegar, and ginger. Season with salt and pepper. Add shrimp, bell pepper, and scallions; toss to combine. Transfer to a rimmed (or toaster-oven) baking sheet, and spread in a single layer.
Heat broiler (or toaster oven). Broil, 4 inches from heat source, until shrimp are opaque throughout, about 3 minutes. Transfer contents of baking sheet to pot; toss with pasta to combine.