Soak top and bottom of 3-1/4 quart clay cooker in water about 15 minutes; drain. Place chicken quarters, skin side up, in clay cooker. Drizzle with lemon juice and vinegar. Sprinkle with tarragon, salt, pepper and shallots. Pour in chicken broth. Place covered cooker in cold oven. Set oven at 450°. Bake until chicken is tender and light brown, about 1-1/4 hours. Pour cooking liquid into medium skillet. Add whiping cream to cooking liquid. Het to boiling; cook, stirring occasionally, until slightly thickened. Pour over chicken.