In a food processor fitted with the blade attachment, combine flour, salt, beets and eggs until a loose dough forms. Turn the dough out onto a floured board and knead to form a ball. Flatten the ball into a disc, wrap in plastic and let rest at room temperature for 1 hour.
Divide the dough into 4 pieces. Cut each piece into quarter-size knobs. Roll each knob on the back of a cheese grater to create notched gnocchi.
In a large pot of boiling water, cook pasta for about 3 minutes until al dente. Serve with sauce of choice.