Preheat the oven to 350°F (175°C) and line a rimmed baking sheet with parchment paper.
Add the shallot, parsley, oregano, garlic, salt, pepper, and red pepper flakes to a food processor. Pulse until finely chopped but still slightly chunky. Stir in the olive oil and red wine vinegar.
Mix ⅓ cup of the chimichurri with the breadcrumbs. Add the beef, pork, eggs, salt, and pepper, then gently mix just until combined.
Form the mixture into golf-ball-sized meatballs, about 2 tablespoons each, and arrange them on the prepared baking sheet.
Bake for 15 minutes. Switch the oven to broil and cook for another 3–5 minutes, until browned and the meatballs reach 165°F internally.
Serve warm with the remaining chimichurri sauce for dipping or spooned over the meatballs.