In a large bowl, combine ricotta, Parmesan, chives, salt, and nutmeg. Mix well. Make a well in the middle and crack egg into center. Mix until fully combined.
Add flour and mix until dough thickens. Divide roughly into six sections.
Generously flour a cutting board or other surface. Roll each of the six sections into a log, about 1 to 1½ inches thick. If log is sticking to surface, dust with more flour.
Cut logs into 1 inch pieces. Place pieces, cut side down, onto a separate floured surface and press down on them with a fork to shape.
Bring a large pot of heavily salted water to boil. Add gnocchi (in batches if crowded), and cook until they float for 1-2 minutes. Using a slotted spoon, transfer them to a large bowl or plate.
Heat olive oil in a large saucepan. Add anchovies and cook until they start to break down, about 2-3 minutes. Stir in garlic cloves and cook until fragrant. Pour in white wine and simmer for 4-5 minutes. Add tomatoes, stir well, and reduce heat. Cook until sauce has thickened, about 15 minutes.
Once sauce is ready, you can add gnocchi into the pan if they need to be reheated or else pour sauce on top of gnocchi.