If using roasted garlic, prepare it in advance by cutting the top off a head of garlic, drizzling with olive oil, and wrapping in parchment paper first, then foil. Roast at 400°F for 30-40 minutes until tender and golden. Let cool, then squeeze out the cloves.
In a food processor, pulse the garlic (roasted or fresh) until finely minced.
Add the fresh basil and broccoli sprouts to the food processor. Pulse until the greens are finely chopped.
With the food processor running, slowly drizzle in the olive oil and lemon-infused olive oil through the feed tube. Process until the mixture becomes a smooth paste.
Add the pine nuts, shaved Parmesan cheese, sumac, and salt to the food processor. Pulse a few times until the nuts are chopped and all ingredients are well combined.
Taste the pesto and adjust seasoning as needed, adding more salt, sumac, or lemon-infused olive oil to suit your preferences.
Transfer the pesto to a jar or airtight container. If not using immediately, pour a thin layer of olive oil over the surface to prevent browning.