Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil and grease with nonstick cooking spray.
Cut beets into spirals using a spiralizer.
Place beet spirals in a bowl; add 1/4 teaspoon salt and 1/8 teaspoon black pepper and toss to combine. Spread out on the prepared baking sheet.
Bake in the preheated oven, stirring halfway, until softened, about 10 minutes. Let cool completely, 5 to 10 minutes.
Whisk olive oil, quince vinegar, salt, and pepper together in a small bowl to make dressing.
Divide spring salad mix between 2 plates. Top with cooled beet spirals. Scatter blue cheese, chopped walnuts, and chives over the beets. Drizzle dressing on top.