The Stiles family poses for a portrait in the pit room of their new restaurant,The Switch, located near Dripping Springs. Left to right, Stella, 6, Shane, Catherine and Ava, 5. (Photo ©Chris Wilkins/Texas BBQ Posse) Barbecue impresarios Shane and Catherine Stiles gave the Posse a sneak peek recently of their new place — The Switch — which they will be opening on Friday June 22, located just off Highway 290 near Dripping Springs. Their original place, Stiles Switch BBQ and Brew in Austin, is one of the best joints in the state. Catherine Stiles, of course, has made her own…