Combine water and ice in a bowl. Preheat a skillet over medium heat; add spinach. Cook, stirring continuously, until spinach turns bright green, about 30 seconds. Plunge into ice water bath; remove when spinach is lukewarm. Squeeze out excess moisture with cheese cloth.
Combine spinach, eggs, olive oil, and salt in a food processor; blend until smooth. Add flour; blend until dough no longer sticks to the blades, adding flour as needed.
Roll dough into a ball; wrap in plastic wrap. Rest at room temperature for 20 minutes.
Remove plastic wrap from dough. Transfer to a work surface generously dusted with flour; cut dough into 4 pieces with a sharp knife. Roll out dough with a rolling pin to 1/4-inch thickness; shape into rectangles.
Dust pasta maker rollers with flour. Run the dough rectangles through a pasta maker on the widest setting. Repeat rolling dough through rollers, gradually reducing the setting to desired thickness. Change pasta maker's attachment to preferred noodle shape; cut pasta with pasta maker.
Bring a large pot of water to a boil. Lower pasta gently into water; use a spoon to keep noodles from sticking together. Cook until pasta is firm but soft, 3 to 6 minutes. Remove from the water with tongs; transfer to a bowl.