Preheat oven to 450 degrees with racks in upper and lower thirds. On a rimmed baking sheet, toss asparagus with 1 tablespoon oil and season with salt and pepper. Roast until tender and browned in spots, about 20 minutes.
Meanwhile,in a large bowl, whisk together mustard, vinegar, chives, 3 tablespoons olive oil, and season with salt and pepper. Brush both sides of bread with vinaigrette, and place on a baking sheet. Bake until both sides are golden, about 8 minutes, flipping once.
Add greens and radishes to bowl, toss to coat, and divide among four plates. Top with asparagus. Season ricotta with salt and pepper and spread on toast to serve.