In a food processor, combine basil, 1/4 cup toasted pine nuts, Parmesan, garlic, lemon juice, salt, and pepper. Pulse until finely chopped. With the motor running, slowly pour in the olive oil until smooth and emulsified. Taste and adjust seasoning. Set aside.
Spiralize the zucchini using a spiralizer with the medium blade. Lay the noodles on a clean kitchen towel or paper towels and gently press to absorb excess moisture. This prevents a watery dish.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the halved cherry tomatoes, cut side down, and let them sear without moving for 2 minutes. Add garlic and red pepper flakes, stir gently, and cook for 30 seconds until the tomatoes just begin to burst. Season with a pinch of salt.
Add the spiralized zucchini to the skillet with the tomatoes. Toss gently with tongs for 1-2 minutes, just until the noodles are slightly softened and warmed through but still have a nice bite. Remove from heat immediately to avoid overcooking.
Spoon dollops of the pesto over the warm zucchini noodles and fold gently until evenly coated. Divide among serving bowls. Top with the remaining toasted pine nuts, fresh basil leaves, and shaved Parmesan. Finish with an extra squeeze of lemon if desired.