01 - Bring a large pot of salted water to a rolling boil. Cook the pasta until al dente, following package directions. Reserve 150 milliliters of the starchy pasta water before draining. Set aside.
02 - In a blender or food processor, combine fresh mint leaves, 60 milliliters of extra-virgin olive oil, and 1/4 teaspoon of flaky sea salt. Process until smooth. Strain the mixture through a fine-mesh sieve, discarding the solids. Transfer the infused oil to a small spray bottle or keep it ready for drizzling.
03 - In a large skillet over medium heat, melt the unsalted butter with 2 tablespoons of extra-virgin olive oil. Add the finely chopped shallot and sauté for 2 minutes until softened. Introduce the minced garlic and cook for an additional 30 seconds until fragrant.
04 - Add the peas to the skillet and sauté for 2 to 3 minutes until heated through (if using frozen peas). Stir in the pea shoots and cook for 1 minute, just until they begin to wilt.
05 - Add the drained pasta to the skillet. Incorporate half of the reserved pasta water and toss vigorously to coat the pasta. Gradually add more pasta water as needed to create a glossy, cohesive sauce that clings to the strands.
06 - Remove the skillet from the heat. Stir in the lemon zest and toss once more. Season to taste with salt and freshly ground black pepper.
07 - Portion the pasta onto individual plates. Finish each serving with a generous mist of the mint oil or a careful drizzle. Garnish with grated Parmesan cheese, if desired, and an extra grind of black pepper.