Trim root ends and tough, dark green tops off leeks. Split leeks lengthwise, rinse with water, and slice thinly to make 1 quart of cut leeks.
In a large, heavy soup pot sprayed with nonstick spray, cook leeks, mushrooms, garlic, tarragon and pepper over medium-high heat, stirring often for 15 minutes. Cover pot if vegetables become too dry.
In a blender, mix flour with milk. Add to cooked vegetables. Add chicken broth and cook over medium heat, stirring constantly, until thickened.