Heat oven to 425 degrees F. With sharp knife, score skin side of duck breasts in a series of parallel cuts 3/4 inch apart, without cutting into meat. Make a second series of parallel cuts perpendicular to the first to form crosshatch pattern.
Season breasts with salt and pepper. Place breasts skin side down in heavy nonstick skillet. Cook over medium heat for about 8 minutes or until fat runs out and skin is golden‐brown and crisp. Transfer breasts to baking dish or another skillet, skin side down, and finish cooking in oven about 10 minutes for medium‐rare and 12 minutes for medium, turning breasts onto flesh side after 6 minutes. Let breasts rest 3 to 4 minutes before slicing.
While duck breasts are in the oven, pour off fat from skillet breasts were browned in. Add broth and simmer until reduced to about 1/4 cup. Add 1 tablespoon of the butter and simmer until slightly syrupy; stir in tarragon, mint and chives. Keep warm over low heat.
In skillet over medium heat, simmer peas, beans, asparagus, artichokes and remaining tablespoon butter in 1/4 cup water, covered, about 5 minutes or until vegetables are tender but still bright green. Place half the vegetables on each of 2 plates, mounding them slightly. Cut each breast crosswise on a slight angle into 4 to 5 slices about 1/2‐inch thick; fan slices around vegetables. Spoon half the sauce over each breast.