For the Slaw: Cut the cabbage in half, then in quarters. Remove the core and discard. Slice each quarter cabbage into ¼ inch thin slices. In a large mixing bowl, whisk together the mayonnaise, vinegar, salt and pepper. Taste for seasoning. Toss the cabbage with the dressing until well coated. Keep refrigerated until ready to use.
For the Topping: In a small bowl, mix the yogurt and pesto until blended well. Fold in the cucumbers. Keep refrigerated until ready to use.
To Assemble the Slaw Dogs:
Place a grilled hot dog on a toasted bun. Spoon on the minted yogurt mixture. Top with a couple of Tablespoons of slaw mix. Finish with a garnish of sliced tomatoes.