Bring a large pot of salted water to a boil for the pasta. Salt it generously — it should taste like the sea.

While water heats, heat 2 tbsp olive oil in a large skillet over medium heat. Add sliced leeks and a pinch of salt. Cook, stirring occasionally, until soft and translucent (5–7 minutes).

Add the smashed garlic to the leeks and cook 30–60 seconds until fragrant. Stir in 1 cup of peas and 2–3 tbsp pasta water (or plain water) to loosen.

Cook pasta until al dente according to package directions. Before draining, scoop and save 1/2 cup of the starchy cooking water.

Transfer the leek–pea mixture to a blender or use an immersion blender and process until smooth and bright green. Return sauce to the skillet.

Add drained pasta to the skillet with the puree. Toss over low heat, adding reserved pasta water a splash at a time until the sauce coats the pasta nicely (about 1–2 minutes). Stir in lemon zest, lemon juice, grated cheese (if using), and remaining whole peas.

If sauce is too thick, add more pasta water; if too thin, simmer gently until reduced.

Plate pasta and top each serving with torn or whole fresh burrata. Drizzle with remaining olive oil, scatter toasted nuts if using, and finish with cracked black pepper and herbs.