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Fill large pot with 3-4 inches water and heat to medium-high heat. Stir in several pinches salt and add potato and beet; Cook 10-12 minutes or until fork tender.
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In colander, strain vegetables and let steam dry a few minutes.
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To food processor, add just the beets and a pinch of salt and pulse until smooth, stopping to scrape sides with spatula.
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To large mixing bowl, add potatoes and mash.
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Add pulsed beets to bowl with potatoes and, using gloved hands, mix well. Add 1 cup flour and mix well. Add 1/2 cup flour and mix. The consistency should be a little sticky.
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Roll dough into ball and place on floured work surface. Begin to knead dough for few minutes adding pinch of flour every so often to avoid sticking.
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Once dough is ready, cut into 4 equal pieces. Roll out each piece into long snake-like shape about 1/2- inch thick and slice each roll into 2-inch pieces.
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In well-salted pot of boiling water, add gnocchi in small batches and cook until they begin to float, about 2-3 minutes. Remove to plate.
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To pan over medium heat, add 3 tablespoons butter and splash of olive oil. Stir and cook over medium-low heat for a few minutes until browned but not burnt.
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Transfer gnocchi to pan with brown butter sauce and cook about 1-2 minutes per side. Continue until all gnocchi are browned. Transfer to plate.
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Drop a few sage leaves into brown butter sauce and cook for 1 minute until crispy.
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Add portion of gnocchi to 4 bowls. Top with brown butter sauce, grated Parmesan cheese and fried sage.