Preheat oven to 425°. Trim leaves from broccolini if you like (for a tidier look). Put broccolini on 2 large rimmed baking sheets.
Combine 3 tbsp. oil with the salt and 1/4 tsp. pepper. Drizzle over broccolini and turn until well coated. Roast, switching pan positions and turning broccolini with tongs halfway through cooking, until browned at edges, about 15 minutes.
Meanwhile, heat remaining 3 tbsp. oil and 1/4 tsp. pepper with the garlic and anchovies in a 12-in. frying pan over medium-low heat. Cook, stirring occasionally, until garlic is soft but not browned (reduce heat if needed), 12 to 15 minutes.
Toss broccolini with anchovy mixture in frying pan. Serve with lemon wedges to squeeze on top if you like.