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Combine flour, salt and pepper in a medium-sized mixing bowl. In a small bowl, whisk together milk, egg and sweet potato puree until homogenous. Add liquid mixture to dry ingredients and stir with a wooden spoon until combined. Allow to sit for 20-30 minutes at room temperature while preparing the pesto.
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To prepare pesto, add garlic cloves and walnuts to a food processor and pulse until finely chopped. Add kale, lemon zest, lemon juice, salt and pepper and pulse again until kale is finely chopped. You made need to use a spatula to scrape down the sides of the bowl as you go. With food processor running, slowly stream in olive oil through the top spout and pulse until smooth and creamy. Add parmesan cheese and pulse briefly, about 10 seconds or so, until combined. Transfer to an airtight container for storage.
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Bring a large pot of salted water to a boil over high heat. Using spaetzle maker (or alternatively, using a colander with larger holes), drop the spaetzle dough into the boiling water and cook just about 45-60 seconds. Remove to a bowl and add a splash of olive oil, tossing to coat.
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Serve spaetzle with pesto and extra parmesan cheese. Enjoy!