Step 1

Trim and rinse the scallions. Cut the green and white parts and chop them separately; set aside the green tops for garnish. Get at least 2 cups water ready by the stove.

Step 2

Put 2 tablespoons of the butter or oil in a large pot over medium heat. When it is hot, add the sliced white part of the scallions and cook, stirring occasionally, until they soften, just a minute or so. Stir in about 1 cup of water. Carefully take a tomato from the can, crush it with your hands and remove the tough core, and drop it into the pot. Repeat with the remaining tomatoes; then pour in the juice. (Or you can cut the tomatoes in the can with scissors or pour the whole can in at once and break them up with a potato masher in the pot.) Sprinkle the sauce with salt.

Step 3

Raise the heat to medium high. When the sauce comes to a boil, stir in the pasta, either whole or broken in half. Keep stirring and tossing until the noodles bend and soften, about 3 minutes. Then stir occasionally to keep them from sticking together. After a few more minutes, when the tomatoes break down and the pot gets dry, start adding water, 1/2 cup at a time, stirring after each addition. When the liquid is just about absorbed, add more. Keep the heat at medium, stir frequently, and repeat adding water as necessary; you’ll need almost all of the 2 cups you measured earlier.

Step 4

Begin tasting the pasta 10 minutes after you added it; the strands should be tender but have some firmness when you bite. (It could take as long as 15 minutes to reach this stage.) When the pasta is ready, stir in the remaining butter or oil and enough additional water to make the noodles glossy and thickly coated. Taste and add more salt and some pepper, spread the pasta into the bottom of the pot, and crack in the eggs.

Step 5

Cover the pot, remove it from the heat and let it sit until the yolks are as runny or solid as you like, 4 to 8 minutes. You can serve the eggs whole, or stir them into the noodles (or do a combination as shown in the photo). To serve, scoop out the noodles with a large spoon and tongs and garnish with the reserved scallion tops. Pass the soy sauce at the table.