Prepare a high gas or charcoal grill fire. Partially split each okra pod lengthwise, leaving about 1/2 inch uncut at the stem end. In a large bowl, toss the okra with the oil, 1 tsp. salt, and 1/4 tsp. pepper.
In a small bowl, combine the sour cream, mayonnaise, shallot, lemon juice, cilantro (if using), smoked paprika, red pepper flakes, and 1/2 tsp. salt; set aside.
Grill the okra, flipping once, until the pods are slightly charred and have just split open, about 5 minutes. Transfer to a large platter (don’t overcrowd the platter as residual heat and steam can soften the pods). Serve the okra hot with the dip on the side.