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McClure's Barbecue Restaurant Review: Launched as a casual pop-up inside Company Burger, McClure’s served barbecue family-style, and became so popular that Neil McClure, former general manager of local favorite Dante's Kitchen, opened this location offering all of the usual suspects: ribs, chicken, sausage, pulled pork, beef brisket, coleslaw, beans and potato salad. A surprisingly outstanding jambalaya is on the menu, too. There is nothing mundane about the flavors. McClure’s six sauces represent different geographical areas, even an Asian variety, and thankfully a Kansas City version. The building is small and the interior is nondescript, but it doesn't matter. What matters is the authenticity of the slow-cooked, fall-off-the-bone tender meats. No desserts and BYOB.