Preheat oven to 400°F. Brush ½ teaspoon oil over a large baking sheet. Cut prosciutto into 1- to 1½-inch squares and place on the baking sheet. Brush the prosciutto with ½ teaspoon oil. Bake until crispy, 5 to 7 minutes. Carefully transfer the prosciutto "chips" to a wire rack with a spatula. (If you leave them on the baking sheet, they won't be as crisp.)
Meanwhile, place beets in a large saucepan with enough water to cover by at least 2 inches. Bring to a boil; reduce heat to maintain a gentle simmer and cook until tender when pierced with a fork, 20 to 30 minutes. (If using larger beets, they will take up to 40 minutes.) Drain and let stand until cool enough to handle. Trim both ends of the beets and rub off the skins. Cut into wedges.
While the beets are cooking, combine onion with the remaining 1 tablespoon oil, thyme, salt and pepper in a small saucepan. Cover and cook over medium-low heat, stirring often, for 10 minutes. Uncover and continue cooking until the onion is very soft and caramelized, 8 to 10 minutes more. (If the onion begins to brown before it becomes very soft, add water 1 tablespoon at a time.) Remove from the heat, cover and let stand for 10 minutes.
Stir the onion, scraping up any browned bits. Set aside ¼ cup and transfer the remaining onion to a food processor or blender. Add buttermilk, vinegar, mayonnaise and chives; puree until smooth.
Toss salad greens, the reserved ¼ cup onion and the dressing in a large bowl. Divide among 6 plates. Top with the beets and prosciutto chips.
Make Ahead Tip: Cover and refrigerate cooked beets (Step 2) for up to 2 days. Bring to room temperature before serving.
127 calories;7 g fat(2 g sat); 4 g fiber; 13 g carbohydrates; 6 g protein; 203 mcg folate; 11 mg cholesterol; 7 g sugars; 0 g added sugars; 3,528 IU vitamin A; 25 mg vitamin C; 91 mg calcium; 2 mg iron; 421 mg sodium; 603 mg potassium
Vitamin A (71% daily value), Folate (51% dv), Vitamin C (42% dv)