Bring the Water to a Boil: Fill a large pot with water and bring it to a rolling boil. Season generously with kosher salt until the water tastes pleasantly salty, like the sea. This is your only opportunity to season the pasta itself.
Crisp the Prosciutto: Place the ¼-inch (6 mm) cubes of prosciutto in a large skillet over medium heat with the olive oil. Cook for 3 to 5 minutes, stirring occasionally, until the edges begin to lightly crisp and the prosciutto is warmed through. Stir in several generous grinds of freshly cracked black pepper, then reduce the heat to low. Leave the prosciutto and olive oil in the skillet, they'll become the flavorful base for the sauce.
3 ounces prosciutto , 1 tablespoon extra-virgin olive oil
Cook the Pasta: Add the pasta to the boiling water and cook until just shy of al dente, about 1 minute less than the package directions. Before draining, reserve 1 cup (240 ml) of the starchy pasta water.
8 ounces spaghetti
Blanch the Peas: During the final 1 to 2 minutes of cooking, add the shelled English peas directly to the pasta water. They need only a quick blanch to become bright green and tender while maintaining their fresh sweetness.
1 pound English peas in their pods
Build the Sauce: Remove the skillet from the heat. In a small bowl, whisk the egg yolks until smooth. Slowly whisk in 2 to 3 tablespoons of the reserved pasta water, 1 tablespoon at a time, to gently warm the yolks. This process, called tempering, helps prevent the eggs from scrambling when they meet the warm pasta.
2 large egg yolks
Combine Everything: Add the drained pasta and peas to the skillet with the prosciutto. Pour in the tempered egg yolks along with the grated Parmigiano-Reggiano. Toss continuously with tongs, adding a few splashes of the reserved pasta water as needed until the cheese melts and the eggs form a silky sauce that coats every strand of pasta.
1 cup Parmigiano-Reggiano
Finish with Freshness: Fold in the chopped chives and watercress just before serving. The residual heat will gently wilt the watercress while preserving its bright color and peppery bite. Taste and season with additional black pepper or salt, if needed.
2 tablespoons fresh chives, Fresh watercress, Kosher salt and freshly ground black pepper
Serve Immediately: Carbonara is at its absolute best the moment it's finishes. Serve immediately with extra Parmigiano-Reggiano and another generous grind of black pepper.