For the pesto: Add all of the ingredients to the bowl of a food processor and pulse until combined.
For the salad: Heat the oven to 450°. Wash the beets, trim the tops and bottoms, then place them whole in a covered roasting pan or on a baking sheet (cover the beets with foil).
Place in the oven and cook for 45 minutes, or until easily pierced with a fork.
Peel the beets while they’re still warm (but not hot) by running under cool water and gently sliding off their skins. Slice the beets into ¼-inch-thick slices and layer on the diagonal across a serving tray.
Top with the crumbled goat cheese, then use a pastry tube or sandwich baggie with a small hole cut across one corner to pipe the pesto around the beets. Garnish with fresh basil and serve.