• 1 lime, cut into wedges, for serving
Pour the canola oil into a saucepan over medium heat. Once the oil shimmers, add the shallot and cook, stirring frequently, until translucent, for 4 minutes. Stir in the lima (frozen works) and kidney beans, barbecue sauce, bourbon, smoked paprika and salt. Reduce the heat to low and cook for 10 minutes, stirring occasionally, until the lima beans are tender and the bourbon flavor has mellowed. Taste, and add more salt as needed.
Halve the avocados and discard the pits (keep the skins on). Brush the cut sides with the extra-virgin olive oil.
Heat a grill pan over medium-high heat (indoors or out). Cook the avocados, cut sides down, until they have dark brown grill marks, for 3 to 4 minutes. Reduce the heat to medium-low, turn the halves over and cook for 5 minutes, until a knife inserted into the center of the avocado flesh comes out hot to the touch.
Place the avocado halves on a platter, cut sides up. Spoon the barbecue beans on each one and top with the cilantro and cucumber. Serve hot, with the lime wedges.