Heat beet greens, figs, and Riesling wine in a large skillet over medium heat until nearly softened, about 7 minutes, stirring often.
Stir spinach, garlic, and butter into the beet greens mixture. Reduce heat to medium-low; cook and stir until spinach is wilted, about 3 minutes. Season with salt.
Sprinkle Parmesan cheese atop vegetables to serve.
