In a food processor fitted with a fine-hole grating attachment (or on the small holes of a box grater), grate potatoes and carrots. Transfer to a large bowl; add scallions and 1 1/2 teaspoons salt. Using your hands, mix thoroughly. Mix in egg and matzo meal until combined. Divide into 8 mounds of equal size.
In a large nonstick skillet, heat oil over medium-high heat, swirling to coat bottom of pan. Add half the potato mounds; flatten each to a 1/2-inch thickness. Cook until golden brown, 2 to 4 minutes per side.
Transfer to paper towels or parchment paper to drain. Repeat with remaining mounds (reduce temperature to medium if browning too quickly). Sprinkle with salt, and serve with sour cream, if desired.
Made by grinding matzo (an unleavened crackerlike bread), matzo meal is used instead of flour to bind pancakes, such as these, and for breading foods before frying.