Preheat oven to 400 degrees. Drizzle beet and garlic cloves with olive oil and rub to coat evenly. Wrap tightly in aluminum foil and roast until tender, about an hour. Unwrap and allow to cool slightly.
Once the beet is cool enough to handle, use a paper towel to rub the skin off of the beet. Slice into quarters and place in the work bowl of a food processor. Peel the roasted garlic and add it to the bowl along with the beet.
Add one tablespoon of olive oil and the hot water. Process until smooth, scraping down the sides of the bowl as necessary.
Add remaining ingredients except olive oil. Process again until smooth. While the machine is running, slowly add remaining 3 tablespoons of olive oil through the feed tube. Continue to process until fully combined, scraping down the sides of the bowl occasionally.
Transfer hummus to bowl. Season to taste with salt. Chill until ready to serve.
To serve, drizzle with olive oil and sprinkle with chopped fresh parsley or chives, if desired.