Bring 4 quarts of water to a rolling boil in a large pot. Add 1 tablespoon of kosher salt. Submerge the spaghetti and cook until 2 minutes before the package-indicated 'al dente' time.

While the pasta is boiling, combine the extra virgin olive oil and the sliced garlic in a large, cold skillet. Place over medium-low heat to gradually infuse the oil.

Sauté the garlic gently, stirring frequently, until the edges are golden brown and the oil is highly fragrant (approximately 5-8 minutes). Do not allow the garlic to turn dark brown or bitter.

Add the red pepper flakes to the oil and cook for an additional 30 seconds to release the capsaicin and color the oil.

Ladle 1/2 cup of the starchy pasta water from the boiling pot directly into the skillet with the oil and garlic. Whisk or swirl vigorously to begin the emulsion process.

Drain the pasta (or use tongs to transfer it directly) into the skillet. Increase the heat to medium-high.

Toss the pasta constantly with tongs for 2 minutes. This mechanical action, combined with the heat and starch, creates the 'mantecatura'—a creamy, cohesive sauce that clings to the noodles.

Remove from heat. Add the chopped parsley and lemon juice (if using). Continue tossing to incorporate.

Fold in the grated Parmigiano-Reggiano immediately before serving to ensure it melts into the emulsion rather than clumping.

Plate immediately, drizzling any remaining garlic oil from the pan over each serving.