Toast the Nuts: In a small skillet over medium heat, toast the pine nuts, stirring occasionally, until they turn golden and release their aroma. This should take about 3–5 minutes. Remove from heat and let them cool slightly.
Make the Pesto: Add the toasted nuts, basil leaves, Parmesan cheese, olive oil, garlic, lemon juice, salt, and black pepper to a food processor. Blend the mixture for about 2–3 minutes, pausing occasionally to scrape down the sides of the bowl, until the pesto is smooth and creamy. Set it aside.
Cook the Pasta: Fill a large pot with water and bring it to a boil over high heat. Add the sea salt and cook the fusilli pasta according to the package directions until al dente. Before draining the pasta, save ½ cup of the cooking water.
Combine Pasta and Pesto: Place the drained pasta in a large mixing bowl. Add about ½ cup of the prepared pesto and toss it with the pasta to coat evenly. Gradually mix in ¼ cup of the reserved pasta water, adding more as needed to reach your desired creamy consistency. Add extra pesto if preferred for a more robust flavor.
Add Garnishes and Serve: Sprinkle the pasta with halved cherry tomatoes and additional pine nuts, if desired. Top with freshly grated Parmesan cheese. Serve immediately while warm.