Preheat oven to 350 degrees F. In a large mixing bowl, cream the butter and brown sugar until light and fluffy. Combine the 1-½ cups flour and the oats; add to the creamed mixture. Reserve 1-½ cups of the mixture for topping. Press remaining crumb mixture onto the bottom of a 13x9x2-inch ungreased baking pan. Bake until lightly brown, about 10 to 12 minutes.
Meanwhile, in a large bowl combine the cherries, sour cream, granulated sugar, egg, 2 tablespoons flour, zest, and vanilla. Stir until well blended. Spread over the hot crust. Sprinkle with reserved crumb mixture. Bake until filling is set and topping is golden-brown, about 20 to 30 minutes. Remove from oven, set pan on rack, and cool completely. Cut into bars. Refrigerate leftovers.