Pulse the garlic in a food processor until it is finely chopped. Then, add the basil, pine nuts, lemon juice, and water and process to a puree.
Add the olive oil and 3 tablespoons of the Parmesan cheese and pulse until the pesto is smooth, occasionally scraping down the side of the bowl as necessary. Set aside.
Cook the pasta according to the package directions, and while it is cooking, flake the smoked trout. After the pasta is cooked, pulse the pesto to make sure it has remained blended, then toss the pesto and trout with the pasta.
Sprinkle the remaining grated Parmesan cheese on top of each serving. Serve immediately.