Preheat oven to 400°. Toss beets and 2 tbsp. oil together in a medium baking dish. Cover with foil and bake until beets are tender when pierced with the tip of a knife, about 25 minutes. Peel beets when cool enough to handle, then halve or quarter, depending on their size.
Whirl butter, remaining 3 tbsp. oil, the anchovies (including oil), and garlic together in a food processor until anchovies and garlic are minced. Transfer to a small saucepan. Simmer over medium-low heat 10 minutes, stirring occasionally. Season to taste with salt. Pour bagna cauda into a small warmed bowl.
Arrange vegetables on a platter and serve with bagna cauda for dunking.