Put the sheet pans in the oven and preheat the oven to 425 degrees F.
Toss the potatoes, parsnips, carrots and garlic in a large bowl with the thyme, rosemary, 3 tablespoons of the olive oil, 2 teaspoons salt and ½ teaspoon pepper until fully coated. Add the vegetables to the hot sheet pan and return it to the oven. Roast, tossing halfway through, until tender and browned, about 30 minutes.
To make the salsa verde, add the parsley, capers, lemon juice and remaining 5 tablespoons olive oil to a food processor and pulse until smooth. Carefully peel the roasted garlic, add it to the food processor and pulse until completely combined.
Serve the vegetables warm with the salsa verde.
