Combine potatoes, egg, flour, salt, and olive oil in a bowl. Knead until dough forms a large ball.

Take small segments of dough and roll into snakes.

Use corn flour to sprinkle on surface and cut the snakes into half-inch pieces.

Bring a large pot of water to a boil, and add salt to taste and one to two tablespoons of olive oil.

Drop in the gnocchi carefully one at a time, and let cook for three to five minutes until they have risen to the top. Remove with slotted spoon and toss in corn flour.

Melt butter in a frying pan.

Add garlic, Parmesan cheese, and mushrooms.

Stir, and add gnocchi over a medium-high heat until golden brown. Remove from pan.

Combine basil, olive oil, garlic, red pepper, and salt in a food processor. Pulse until smooth, adding olive oil as needed to reach desired consistency.

Plate with pan-fried gnocchi and top with pine nuts.