For the pasta, combine a few tablespoons of water and salt in a small bowl. Pour flour out onto a work surface. Create a well in the center of the flour. Pour eggs into well. Add 1 tablespoon of salted water to the eggs (you may use more later on if dough seems too dry). Drawing flour from the outside in towards the center, begin combining the eggs and the flour, using a fork or your hands. Continue until a uniform dough begins to form, adding more salted water if necessary, 1 tablespoon at a time. Knead the dough for at least 10 minutes. The dough should feel smooth. When you press your thumb into the dough, it should spring back. 

Wrap dough in plastic wrap and let rest at room temperature for 30 minutes. 

Meanwhile, make the marinara sauce: Heat olive oil in a medium pan or dutch oven over medium-high heat. Add onion and carrot and cook until softened, about 8 minutes. Add tomatoes, parsley, and grated nutmeg. Season with salt and pepper. Simmer sauce for 30 minutes. 

After resting the dough, roll the pasta into a very thin sheet. Let air dry for about 15 minutes. Carefully roll up, making sure not to press the dough into itself. Using a very sharp straight edge knife, cut the rolls cross-wise into skinny strips (the width you want pasta to be) then unfurl.

Bring a large pot of salted water to a boil. 

Cook the spaghetti for about 5 minutes, until tender. Drain.

Serve with marinara sauce and grated cheese.