Sweet Onion and Fried Chicken Salad

1 large head leaf lettuce, or a combination of lettuces 

8 halved cherry tomatoes 

1/2 c. sliced mushrooms 

1/2 c. peanut oil 

1 c. all-purpose flour 

1/2 tsp. salt 

1/4 tsp. coarse-ground black pepper 

1/3 c. milk 

2 whole chicken breasts, halved, boned, and cut into 1/2-inch strips 

2 T. white wine vinegar 

1 tsp. Dijon mustard 

1 minced shallot 

1 T. fresh or 1 tsp. dried tarragon 

1 Texas 1015 onion, sliced thin 

Arrange lettuce leaves, tomatoes, and mushrooms on a large salad plate. Heat oil in a frying pan on medium-high heat. In a shallow bowl, mix flour with salt and coarse pepper. Put milk in separate bowl. Dip chicken strips into milk and then into flour mixture to coat. Fry chicken on both sides until golden brown, about 5 minutes total. Drain chicken on paper towels; save oil in pan. Add vinegar to oil. Stir, scraping pan. Pour vinegar into mixing bowl, add mustard and mix. Add shallot and tarragon; season to taste. Place chicken and sliced onion on top of salad. Serve dressing on the side.