To prepare crema: Whisk yogurt, lime zest, lime juice, ⅛ teaspoon chili powder and a pinch of salt in a small bowl. Set aside.
To prepare quesadillas: Bring about 1 inch of water to a boil in a large saucepan fitted with a steamer basket. Add beet, cover and steam until fork-tender, 8 to 10 minutes. Transfer to a medium bowl and toss with chili powder, salt and pepper; lightly mash with a fork.
Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add garlic and cook, stirring, for 30 seconds. Add beet greens (or spinach) and cook, stirring, until slightly wilted, 1 to 2 minutes. Stir the greens into the mashed beets. Wipe out the skillet.
Spoon about ⅓ cup of the beet mixture and a scant ¼ cup goat cheese onto each tortilla; fold closed.
Using 1½ teaspoons oil per batch, cook quesadillas in the skillet over medium heat, 2 at a time, until lightly browned, 3 to 4 minutes per side. Serve with the crema.
Make Ahead Tip: Refrigerate crema (Step 1) and beet mixture (Steps 2-3) separately for up to 2 days.
322 calories;16 g fat(6 g sat); 4 g fiber; 32 g carbohydrates; 12 g protein; 45 mcg folate; 17 mg cholesterol; 7 g sugars; 0 g added sugars; 2,107 IU vitamin A; 10 mg vitamin C; 214 mg calcium; 3 mg iron; 672 mg sodium; 360 mg potassium
Vitamin A (42% daily value), Calcium (21% dv)