Place the trimmed beets in a metal baking pan filled ½ inch deep with water. Cover with foil.
Roast until the beets are easily pierced with a fork, about 1 hour 20 minutes (depending on the size of the beets). Remove the beets from the pan and let them rest until they are cool enough to handle.
Using your hands, slip the skins off of the beets, and cut the beets into ½-inch cubes.
In a large bowl, gently toss together the beets and celery.
In a small bowl, whisk together the balsamic vinegar, olive oil, salt and pepper. Pour about ⅔ of the dressing over the beet salad. Taste and add more dressing, if desired.
Stir in the basil.
Crisps:
Preheat the oven to 350 degrees F. Line a large baking sheet with parchment paper or a Silpat.
In a medium bowl, mix together the Dubliner cheese, flour and cayenne pepper.
Using 1 tablespoon of the cheese mixture for each crisp, spread the cheese in a small circle, being sure not to spread it too thin. Leave about ¾-inch between each crisp.
Bake until the cheese is bubbling and golden brown, 6 to 7 minutes. Remove from the oven and carefully transfer each crisp to a wire rack. Cool completely (they will harden as they cool).
Serve each portion of salad with 1-2 cheese crisps.