Bring eight cups of water to a boil in a large saucepan. Thinly slice 2 of the Garlic (2 clove) into quarter inch slices, and set aside. Cut the Red Creamer Potato (8 ounce) in half, then cut each half into four pieces.
Trim ends off the Green Beans (6 ounce) and cut into one inch pieces. Set aside. Pick the Fresh Basil (1 ounce) leaves from stems and discard stems. Set leaves aside.
Zest the Lemon (1) onto a plate, and set aside. Juice lemon into a small bowl. Using a fork, remove seeds. Set juice aside.
When water reaches a boil, add potatoes and cook for two minutes.
Then, add sliced garlic and cook for an additional two minutes.
Add the Spaghetti (6 ounce) to the saucepan and cook for nine minutes, stirring occasionally. In the last two minutes of cooking, add the green beans. In a colander, drain the pasta well and return to the saucepan.
To create the pesto, pour Olive Oil (1/4 cup), basil leaves, half of the Pine Nuts (2 tablespoon), the last clove of Garlic (1 clove), one tablespoon of Parmesan Cheese (2 tablespoon), Salt (1/2 teaspoon), and Ground Black Pepper (1/2 teaspoon) into the bowl of a food processor.
Blend until smooth.
Add the pesto to the pot with the pasta and vegetables and toss until well incorporated. Add the lemon juice and half of the zest. Toss.
Place the spaghetti in the center of two plates. Garnish with the remaining parmesan, pine nuts, and lemon zest.