Combine basil, garlic, salt, lemon juice, and pine nuts in a food processor. Process until completely broken down. Then add the artichokes in and pulse until combined.
Turn the processor on low speed and slowly drizzle the olive oil into the pesto until it reaches the desired creamy texture. Typically, I add ½ cup of olive oil, maybe a little more. Then stir in the Parmigiano.
Bring a large pot of water to a boil. Add the spaghetti and boil until al dente.
In a large saucepan, add 2 tablespoon olive oil over medium-low heat. Once hot, add the garlic and crushed red pepper. Sauté for 1 minute or until the garlic is fragrant. Then stir in the chopped artichokes and stir for another minute. Squeeze in the lemon juice and transfer ½ a cup of the pasta water to the pan.
Drain the spaghetti and add it to the pan. Combine well with the oil and garlic. Remove the pan from the heat and stir in the pesto. Combine well and add another ½ cup of pasta water to make the pasta creamier. Sprinkle with Parmigiano and pine nuts to serve.
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Notes
Use artichokes packed in water, not marinated in olive oil. Marinated artichokes can have different flavors depending on the brand and will add an unnecessary tangy flavor to the pesto.
Drain artichokes well before adding them to pesto.
When you saute the garlic, cook it low and slow so it doesn't burn. Be prepared to add the pasta water so you can stop the garlic from overcooking.
Remove the pan from the heat before adding pesto. If the pan is hot, the cheese will begin to clump and stick to the pan.