Preheat the oven to 400 degrees F (200 degrees C).
Rub beets with olive oil, season with salt, and wrap in foil. Cut the top off garlic and drizzle with olive oil and salt. Wrap garlic tightly in foil. Place beets and garlic on a rimmed baking sheet.
Roast in the preheated oven until garlic is golden and soft and beets are completely fork-tender, about 45 minutes. Remove from oven and cool for 15 to 20 minutes. Peel beets and cut into large chunks. Remove 2 tablespoons of goat cheese and set aside.
Reserve 1 tablespoon goat cheese for topping; place the rest in a food processor. Add roasted beets and garlic, 2 tablespoons olive oil, balsamic vinegar, sea salt, pepper, rosemary, and thyme in a food processor; process until very smooth, about 1 minute, scraping sides of the bowl as needed. Adjust seasoning to taste and spoon into a shallow serving dish.
Sprinkle with the reserved goat cheese, slivered almonds, and basil leaves. Drizzle with balsamic vinegar and olive oil.
