Preheat the oven to 400°. In a large ovenproof skillet, heat the vegetable oil. Add the sunchokes, cut side down, and cook over moderately high heat for 1 minute. Transfer the skillet to the oven and bake for about 25 minutes, until the sunchokes are golden brown and tender.
Meanwhile, in a small saucepan, heat the olive oil. Add the anchovies, garlic and crushed red pepper and cook over low heat until the anchovies are sizzling, about 1 minute. Remove from the heat and stir in the butter, 1 tablespoon at a time. Stir in the lemon juice and season with salt and pepper. Transfer to a shallow bowl and keep warm.
Spoon the sunchokes onto a platter. Garnish with the parsley and serve with the warm bagna cauda and lemon wedges.