Preheat oven and cook pasta Preheat oven to 425°F. Cook pasta in a pot of salted boiling water 4 minutes.
Add broccoli: Add broccoli to pot and cook 2 minutes more; drain broccoli and pasta.
Make topping: Combine panko and 2 tablespoons Parmigiano.
Cook bacon: In a saucepan, cook bacon over medium heat until crisp, 4 to 5 minutes. Transfer to paper towels.
Make sauce: Add butter to pan; melt. Whisk in flour; cook 1 minute. Slowly whisk in milk. Bring to a simmer; cook, whisking, until thickened slightly, about 4 minutes.
Add cheeses, artichokes, broccoli, pasta and bacon to sauce: Stir in remaining Parmigiano, cheddar, artichokes, broccoli, pasta, and bacon; season to taste.
Assemble dish and bake: Transfer mixture to a 2-quart baking dish. Sprinkle with panko mixture. Bake until golden and bubbling, about 20 minutes. Let cool slightly before serving.
