01 - Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
02 - Toss the beet cubes with olive oil, salt, and pepper. Spread evenly on the prepared baking sheet and roast for 25–30 minutes, turning halfway through, until tender and caramelized.
03 - While the beets are roasting, bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Reserve 1/2 cup of pasta water, then drain.
04 - In a nonstick skillet, combine walnuts, sugar, water, and a pinch of sea salt over medium heat. Stir constantly until the sugar melts and coats the walnuts, approximately 3–4 minutes. Transfer the candied walnuts to parchment paper and allow them to cool completely.
05 - In a large bowl, combine the roasted beets, hot pasta, crumbled goat cheese, lemon juice, and lemon zest. Gradually add the reserved pasta water, stirring until a creamy sauce forms and coats the pasta.
06 - Season with freshly ground black pepper and toss gently. Divide the pasta among plates and top with the cooled candied walnuts and chopped chives, if using. Serve immediately.