How to Make It
Fill 2 large bowls with ice water. Bring a large pot of salted water to a boil. Add the asparagus and cook until it is crisp-tender, 2 to 3 minutes. Transfer the asparagus to a bowl of ice water to cool; drain well and pat dry.
Return the water in the pot to a boil. Add the broccoli rabe and cook until crisp-tender, about 2 minutes; drain. Immediately plunge the broccoli rabe into the other bowl of ice water to cool. Drain well and pat dry.
In a medium saucepan, melt the butter in the olive oil over moderately low heat. Add the anchovies and garlic and cook until the garlic is fragrant and opaque, 2 to 3 minutes; season with salt and pepper. Pour the bagna cauda into a heatproof dish or a fondue pot. Arrange the vegetables on a platter and serve with the warm bagna cauda.