Preheat oven to 350°. Spread almonds in a single layer on a rimmed baking pan. Roast almonds until golden and fragrant, about 10 minutes. Cool to room temperature.
In a food processor, finely chop garlic. Add almonds and whirl until coarsely chopped. Add parsley, oil, salt, and chile flakes and whirl until parsley is finely chopped. Add parmesan and pulse to combine.
Preheat oven to 425°. Trim leaves from broccolini if you like (for a tidier look). Put broccolini in a single layer on 2 large rimmed baking sheets.
Drizzle 3 tbsp. oil over broccolini, sprinkle with salt and pepper and turn until well coated. Roast, switching pan positions and turning broccolini with tongs halfway through cooking, until browned at the edges, 20 to 25 minutes.
To serve, spread a layer of pesto on a platter. In a bowl, gently toss broccolini with more pesto and arrange on platter.
Make ahead: Pesto, up to 1 day, chilled. Bring to room temperature before using.