Smash the garlic clove, sprinkle with 1 teaspoon salt and mash into a paste using the flat side of a large knife. Put the garlic paste in a large bowl and stir in the olive oil and lemon juice. Add the pepperoncini and dill, and toss to combine. Add black pepper to taste, toss again and set aside.
Shred the cooked rotisserie chicken using two forks. Add the shredded chicken to the bowl with the dressing and toss to coat.
Cut a diagonal slice across the top of each dinner roll, being careful not to cut all the way through.
Nestle one tomato slice and two cucumber slices into each top-sliced roll. Add a spoonful of the shredded chicken mixture to each roll, in between the tomato and cucumber slices.
Garnish with fresh dill and serve.
Adapted from www.foodnetwork.com