Remove and discard the husks and silk from 2 to 3 large ears fresh corn. Cut the kernels off the cobs until you have 2 cups and transfer to a bowl.

Place the corn cobs in a large pot, add 12 cups (3 quarts) water, and bring to a boil over medium-high heat. Boil for 15 minutes. Meanwhile, cut 8 ounces thick-cut sliced bacon crosswise into ½-inch-wide pieces. Finely grate 1 ½ ounces Pecorino Romano and 1 ounce Parmesan cheese on a Microplane (about 1 cup each).

Remove the cobs from the pot with tongs. Add 1 pound dry spaghetti and 2 teaspoons kosher salt to the corn broth. Cook according to package directions until the pasta is just al dente, 8 to 12 minutes. Meanwhile, place the bacon in a large skillet. Cook over medium heat, stirring occasionally, until browned and crisp, 8 to 10 minutes. Add 1 cup of the corn kernels and 1 teaspoon coarsely ground black pepper. Cook until the corn is well coated and crisp tender, about 1 minute. Turn off the heat.

Transfer the spaghetti with tongs to the skillet — it’s OK if some water clings to the pasta. Toss well to coat the pasta and set aside to cool slightly.

Place the remaining 1 cup corn kernels and ⅓ cup of the hot corn broth in a blender and blend until very smooth. Pour through a fine-mesh strainer set over a medium heatproof bowl, pressing on the solids; discard the contents of the strainer.

Add 4 large eggs to the corn puree and whisk well to combine. Add the Pecorino and Parmesan cheeses and whisk again. While tossing the pasta constantly with tongs, slowly start pouring the egg mixture into the skillet, pouring over the noodles and not the edges of the pan. Add 2 tablespoons of the pasta water, return the pan to low heat, and continue to cook, tossing constantly, until the sauce starts to thicken and coats the pasta, 3 to 6 minutes (add more pasta water a tablespoon at a time as needed if the pan is dry). Move the skillet around the burner to avoid any hot spots that could scramble the eggs.

Take the skillet off the heat. Taste and season with more kosher salt and black pepper as needed. Transfer to a large bowl or individual serving bowls and serve immediately with a few grinds of pepper on top if desired.