Cook pasta in salted water according to the package instructions until al dente. Reserve 2 cups of pasta cooking water.: The pot should be at a vigorous boil so the pasta moves freely and releases starch, which later helps the sauce cling to each piece. You will smell warm wheat and see the surface dancing with steam as it approaches doneness. Taste a piece to check for that slight chew, not limp softness, and be ready to stop cooking a minute before you think; carryover will finish it. A common error is under salting the water, which yields flat tasting pasta , so add enough salt to make the water taste like the sea.
In the same saucepan after you have removed the pasta and the water, add olive oil and melt the butter over medium heat.: The starchy water looks slightly cloudy and will feel silky between your fingers. It is the secret binder for the sauce, giving body and helping the pea purée adhere to the pasta . Keep it hot so it integrates smoothly into the sauce. Avoid draining and discarding all the water or your sauce may be too dry and won’t emulsify well.
Saute the onion for 4 minutes stirring constantly until it’s soft and translucent, add the garlic and cook for 30 more seconds.: You will see the butter foam and then settle, releasing a rich aroma that signals it is ready. Combining olive oil with butter raises the burn point and balances flavor, giving a luscious mouthfeel. Maintain medium heat to prevent butter from browning prematurely. A frequent mistake is using too high heat, which will scorch the butter and impart a bitter note.
Add the frozen peas, and cook for 2 minutes. Add the reserved pasta water, mint leaves, and season with salt and pepper. Cook for 1 minute until the pasta water has been warmed.: As the onion sweats, it will become glossy and smell sweet and savory, a scent that fills the kitchen with warmth. Add the minced garlic when the onion is soft so the garlic releases its aroma without burning; this brief cook time preserves its delicate flavor. Stirring helps the pieces soften evenly. Avoid chopping the onion too coarsely, which leads to uneven cooking and raw pungency.
Blend the peas until you get a smooth sauce, then combine with the pasta.: When the frozen peas hit the pan they will hiss slightly, then quickly return to a vibrant green. The reserved hot pasta water warms the peas and begins to dissolve starches that thicken the sauce. Add torn mint leaves so their oils infuse the mix without becoming bitter. Taste and adjust seasoning carefully, because salt and pepper shape the bright flavors. Resist overcooking the peas into a lifeless mush.
Serve pasta with extra peas, and freshly grated parmesan.: The sauce will become vividly green and silky, with a sweet vegetal perfume. When blended, drizzle some reserved pasta water to reach a sauce that coats the back of a spoon. Toss the pasta vigorously in the sauce so each piece becomes evenly coated, checking texture and adding liquid sparingly to achieve a glossy finish. One misstep is adding too much water at once, which thins the sauce and dilutes flavor, so add gradually.
Serve pasta with extra peas, and freshly grated parmesan: The final plate should present a pop of bright whole peas and a dusting of freshly grated parmesan , which melts slightly onto warm pasta. You will notice a pleasing contrast between the smooth purée and the occasional whole pea. Finish with a crack of pepper if you like a faint heat. Avoid letting it sit too long before serving, as the sauce will thicken and the texture will lose its lively sheen.