Bring a pot of water to a boil. Salt it generously. You want the water to taste like the sea so your pasta is well-seasoned from the start.
Prep the zucchini. Slice into 1/4-inch planks or rounds. Toss with 1 tablespoon olive oil, a generous pinch of salt, and black pepper.
Toast the nuts. In a dry skillet over medium heat, toast pine nuts or walnuts for 2–3 minutes until fragrant and lightly golden.
Shake the pan often to avoid burning. Set aside to cool.
Grill the zucchini. Heat a grill pan or outdoor grill to medium-high. Cook zucchini 2–3 minutes per side until tender with nice grill marks.
If you don’t have a grill, sear in a hot skillet. Drizzle with a squeeze of lemon while warm. Set aside.
Cook the pasta. Add pasta to boiling water and cook until al dente. Reserve 1/2 cup of pasta water before draining.
Make the small-batch pesto. In a food processor or mortar and pestle, combine basil, toasted nuts, garlic, lemon zest, 2 tablespoons olive oil, 1/4 teaspoon salt, and a pinch of red pepper flakes.
Pulse until coarse. Add Parmesan and 1–2 more tablespoons olive oil, pulsing until just combined. Adjust with a splash of lemon juice to taste.
Emulsify the sauce. In a large bowl, add pesto and 2–3 tablespoons of the hot reserved pasta water.
Stir to loosen to a creamy consistency.
Toss the pasta. Add drained pasta to the bowl and toss vigorously. Add more pasta water a splash at a time until every piece is glossy and well coated. Taste and adjust salt, pepper, and lemon.
Plate with zucchini. Divide pasta between two bowls.
Top with warm grilled zucchini, more Parmesan, a drizzle of olive oil, and extra red pepper flakes if you like.
Optional finishing touches. Halve a few cherry tomatoes and toss them with a pinch of salt and olive oil, or scatter a handful of arugula over the top for a peppery bite.