In a large mixing bowl, combine 2 cups of all-purpose flour and a pinch of salt, creating a small well in the center. Crack 3 large eggs into the well, adding a drizzle of olive oil. Using a fork, gently whisk the eggs, gradually incorporating the flour until a shaggy dough forms. Knead the dough on a lightly floured surface for about 10 minutes until it becomes smooth and elastic.

Once kneaded, wrap the pasta dough in plastic wrap and let it rest for 30 minutes at room temperature.

After the dough has rested, divide it into four pieces for easier handling. Using a pasta machine or rolling pin, flatten one piece to about 1/16 inch thick, dusting with flour to prevent sticking. Repeat this process with all pieces, aiming for sheets that are slightly translucent.

Bring a large pot of salted water to a rolling boil and carefully add the freshly cut pasta. Cook for about 2-4 minutes, tasting for doneness; it should be al dente but tender.

In a large skillet over medium heat, add 2 tablespoons of olive oil and 3 minced garlic cloves. Sauté for about 1-2 minutes, just until the garlic is fragrant but not browned. Next, pour in 1 cup of low-sodium chicken broth and the juice of 1 fresh lemon. Stir in 2 tablespoons of capers and allow the sauce to simmer for about 5 minutes.

Add the drained pasta to the skillet with the sauce, tossing gently to combine. If the sauce seems too thick, add a splash of the reserved pasta water for a silky texture. Cook together for an additional minute to warm through.