Place spinach, water, and 1 pinch salt in a pot over medium-high heat; cover pot and cook until spinach is completely wilted, 2 to 3 minutes. Drain; completely squeeze out water. Cool spinach in a colander to room temperature.

Soften ricotta cheese in a large bowl using a fork until creamy.

Squeeze out any excess water from cooled spinach; finely chop with a knife or process in a blender. Transfer to bowl with ricotta; stir in Parmesan cheese, egg, nutmeg, salt, and black pepper.

Divide pasta dough into 6 equal pieces; flatten 1 piece between your palms, cover remaining 5 pieces with plastic wrap. Press flattened dough piece through widest setting on pasta machine. Sprinkle flour over flattened pasta dough, fold in half lengthwise; run through pasta machine again. Repeat process 3 or 4 times until dough is smooth and even in size.

Change pasta machine to middle setting; pass dough through. Change pasta machine to next to last setting; pass dough through. Cut dough sheet in half, crosswise. Pass each half through pasta machine on thinnest and last setting, creating 2 long, very thin sheets; gently transfer to a floured work surface, trimming edges.

Cut dough into 1 ½-inch squares. Drop 1 teaspoon ricotta filling in middle of each square. Brush edges with water; fold over diagonally into a triangle shape. Press well to squeeze out any air. Stretch 2 ends of triangle, fold together, wrapping them around your finger; seal. Gently fold back top corner.

Transfer tortellini to a floured plate or work surface. Repeat with remaining dough and filling. Let tortellini stand for 30 minutes.