Score the fat of the duck in a criss-cross pattern, making sure not to cut into the meat. Season with salt and pepper.
Heat 2 tablespoons oil in a heavy frypan and add the duck skin side down. It should be hot enough to sizzle but not burn. Cook 8 minutes then turn over and cook another 2 minutes. Remove and let rest 3 minutes.
Divide the lettuce leaves between two plates. Scatter the radishes and carrots over the lettuce.
To make the dressing, put the mustard and vinegar in a bowl, season with salt and pepper, and whisk. Slowly pour in the olive oil while still whisking.
Slice the duck breast on the diagonal. Drizzle the dressing over the salad and arrange the duck slices on top.