Preheat oven to 375°F (190°C). Wrap beets individually in aluminum foil and roast for 45-50 minutes until fork-tender.
Allow beets to cool slightly, then peel and blend with egg until completely smooth.
In a large bowl, combine the beet purée, ricotta cheese, flour, and salt. Mix until a soft dough forms.
Turn dough onto a floured surface and knead lightly for 1-2 minutes. Cover and let rest for 15-20 minutes.
Divide dough into 4 equal portions. Roll each portion into long ropes about ¾-inch thick, then cut into 1-inch pieces.
Bring a large pot of salted water to boil. Add gnocchi and cook until they float to the surface, approximately 5-6 minutes. Drain immediately.