Preheat the oven to 350 degrees F. Slice the bagels in 4 across the center and place on 2 baking sheets.
Crush the fennel, mint, oregano, salt and pepper in a mortar and pestle or mini processor. Transfer to a small bowl and add the olive oil and melted butter. Brush the flavored oil and butter mixture onto the bagel pieces.
Bake until toasted and fragrant, about 8 minutes. Serve with your favorite dip.