Pasta Primavera With Asparagus and Peas

Ingredients

• ¼ pound sugar snap peas, stems trimmed
• ½ pound asparagus, ends snapped
• 2 tablespoons unsalted butter
• ¾ cup fresh English peas
• ¼ cup thinly sliced spring onion, white part only (or use shallot)
• 2 garlic cloves, finely chopped
• ½ teaspoon fine sea salt, more as needed
• Black pepper, more as needed
• 12 ounces fettuccine or tagliatelle, preferably fresh
• ⅔ cup grated Parmigiano-Reggiano, at room temperature
• ½ cup crème fraîche or whole milk Greek yogurt, at room temperature
• 3 tablespoons finely chopped parsley
• 1 tablespoon finely chopped tarragon