Preheat the oven to 400℉. Prepare a small baking sheet.
Prep the beet – Scrub the beet clean and trim the ends. Place it on a piece of foil, drizzle with olive oil, and wrap it up so it’s fully sealed.
Prep the garlic – Slice about ¼ inch off the top of the head to expose the cloves. Set it on foil, drizzle generously with olive oil, letting it soak into the exposed cloves, sprinkle with salt, and wrap into a pouch so it's fully sealed.
Roast and Cool – Place both foil packets on a baking sheet and transfer to the oven. Roast for 40–50 minutes, until the garlic is soft and golden and the beet is fork-tender. Let cool for at least 10 minutes. Unwrap the beet and rub off the skin (it should slide right off), then roughly chop into 4 pieces. Squeeze the roasted garlic cloves out of their skins (you can squeeze this right into the food processor).
Blend the dip – Add the roasted beet, roasted garlic, a can of drained white beans, feta, a handful of herbs (chives, basil, or dill), a big squeeze of lemon juice, olive oil, salt, and pepper to a food processor. Blend until smooth and creamy, scraping down the sides as needed. Taste and adjust with more lemon, salt, or olive oil until it’s bright and balanced. Serve with more crumbled feta on top or chopped herbs, with warm pita, crackers, or veggies.