Preheat oven to 400 degrees F. Grease a 1½-quart casserole dish; set aside.
Heat the olive oil over medium-high heat in a large skillet. Add the red pepper and onion and cook until softened and all moisture has evaporated, about 5 minutes. Add the garlic and cook for an additional 30 seconds to 1 minute, or until fragrant. Remove the mixture to a large bowl and allow to cool.
Add the rest of the dip ingredients to the bowl with the pepper mixture and gently stir together until combined, being careful not to smash the crab meat too much. Transfer the mixture to the prepared casserole dish.
With a fork, toss together the bread crumbs, Parmesan and melted butter and sprinkle evenly over the top of the dip.
Bake for 20 minutes, or until golden brown and bubbly. Allow to rest for 10 minutes before serving. Serve with baguette slices or your favorite tortilla or pita chips. Refrigerate any leftovers in an airtight container for up to 2 days.