Step 1

Bring a large pot of salted water to a boil. Combine the sun-dried tomatoes, 1/4 cup water and 1/4 teaspoon liquid smoke in a small bowl. Microwave until the tomatoes are very plump, about 1 minute. Let cool, then strain through a fine-mesh sieve, saving the infused water.

Step 2

Whisk the eggs and egg yolks in a medium bowl with the cheese, miso, remaining 3 to 4 drops of liquid smoke, a pinch of salt and 1/2 teaspoon pepper; set aside.

Step 3

Add the spaghetti to the boiling water and cook as the label directs for al dente. Reserve 2 cups cooking water, then drain.

Step 4

Meanwhile, combine the olive oil, sun-dried tomatoes and garlic in a large nonstick skillet over medium heat. Cook until the tomatoes are sizzling and the garlic is toasted, 2 to 3 minutes. Reduce the heat to low; add the spaghetti, reserved tomato soaking water and 3/4 cup pasta-cooking water and toss. Add the egg mixture and immediately toss until the cheese melts and the sauce starts to thicken; the sauce should be smooth and coat the spaghetti. Gradually add more of the reserved cooking water as needed if the sauce is too thick or clumpy; if you run out of cooking water, use hot tap water. Season with pepper.