In a glass baking dish, combine the chopped beets, the whole garlic cloves and 1 Tb. olive oil. For an oil free dip, use 1 TB. vegetable broth or water instead of the oil.
Bake the beets and garlic for 50 minutes at 425F. Stir occasionally to keep the beets from drying out.
While the beets are baking, toast the walnuts: Place the walnuts in single layer in a pan on the stove top. Cook over medium-high heat for about 5 minutes, stirring or shaking the pan to keep the walnuts from burning. The walnuts will smell toasted and will have just started to brown when they are ready. Remove the toasted walnuts from the pan and allow them to cool.
When the garlic and beets have cooked, place them in a blender along with the toasted walnuts, the balsamic vinegar and the water. Blend until smooth. Store this dip in the refrigerator and serve chilled with crackers or veggie slices.