Preheat oven to 425 degrees. Process bread in a food processor until fine crumbs form. Transfer to a rimmed baking sheet. Toast for 8 minutes.
Cook broccoli in a large pot of boiling water until slightly tender, about 2 minutes. Transfer to a bowl using a slotted spoon, reserving water in pot. Add pasta to water, and cook until al dente, about 8 minutes. Drain.
Add oil and onion to clean pot over medium heat. Saute, stirring occasionally, until onion is translucent, about 7 minutes. Add flour and ground mustard. Cook, stirring constantly, for 1 minute. Whisk in the milk in a slow, steady stream. Bring to a boil. Cook, whisking, for 5 minutes. Remove from heat. Add cheeses and 1 teaspoon salt. Season with pepper.
Stir in broccoli and pasta. Transfer to six 1 1/2-cup ramekins or an 8 1/2-by-11-inch baking dish; top with breadcrumbs. Bake until bubbling and tops are browned, 25 to 30 minutes.