Bring a large pot of generously salted water to a boil. While it heats, whisk together the egg yolks, the whole egg, the grated Pecorino, and the cracked black pepper in a medium bowl until smooth and combined. Set this bowl near the stove where it is warm but not hot.

Heat the olive oil in a large wide skillet over medium heat. Add the garlic and cook for 1 minute until it smells fragrant and turns pale gold. Do not let it brown or it will turn bitter.

Add the zucchini strips to the pan in a single layer if possible. Sprinkle with the salt. Cook for 4 to 5 minutes, tossing occasionally with tongs, until the strips are tender and a few edges have a little color. Remove the pan from the heat and set aside.

Drop the pasta into the boiling water and cook until just al dente, about 1 to 2 minutes less than the package says. Before draining, scoop out at least 1/3 cup of the starchy pasta water and add it slowly to your egg and Pecorino bowl, whisking constantly. This tempers the eggs and helps them become a sauce rather than scramble later.

Drain the pasta and immediately add it to the skillet with the zucchini. The pan should be completely off the heat. Toss the pasta with the zucchini for about 30 seconds using tongs so it picks up any remaining oil and the pan cools just slightly.

Pour the egg and cheese mixture over the pasta. Toss quickly and constantly with the tongs. Add a tablespoon of the reserved pasta water at a time, tossing between each addition, until the sauce becomes glossy and clings to every strand of pasta. This usually takes 2 to 3 tablespoons of pasta water and about 1 minute of steady tossing.

Taste and add more cracked pepper or a pinch of salt if needed. Divide into warm bowls right away. Carbonara sets up as it sits, so do not let it wait. Top with more Pecorino and a generous crack of black pepper at the table.