Preheat your grill or grill pan to medium-high.
Place the peeled garlic cloves on a small square of foil, drizzle with ⅛ tsp. olive oil, and wrap them into a flat package.
Grill for about 20 minutes until soft and fragrant. Open the packet carefully and let the garlic cool slightly.
While the garlic grills, bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente. Important: Reserve about a cup of pasta water before draining.
In a dry skillet over medium heat, toast the sunflower seeds for 5-6 minutes, stirring frequently, until they are golden and aromatic.
Transfer them to a plate to cool.
If using skewers, thread the cherry tomatoes onto them.
Brush the tomatoes and zucchini slices with 2 Tbs. of olive oil.
Grill for about 6 minutes, turning once, until the tomatoes begin to blister and shrink and the zucchini is tender with nice grill marks.
In a food processor, combine the grilled garlic, fresh basil, and 2 Tbs. of the toasted sunflower seeds. Pulse until finely ground.
Add 1 cup (240 ml) of the grilled zucchini, the remaining 1½ Tbs. olive oil, and the grated Parmesan.
Blend until the pesto is smooth and creamy. If it's too thick, add a splash of the reserved pasta water to reach your desired consistency.
In a large bowl, toss the drained pasta with the zucchini pesto until well-coated. Gently fold in the remaining grilled zucchini slices and the grilled cherry tomatoes.
Serve immediately, sprinkled with the remaining toasted sunflower seeds.
Don't skip reserving the pasta water! The starchy water is the secret to emulsifying the pesto and creating a perfectly silky sauce if it seems too thick.
