Drain the artichoke hearts well and gently blot them dry. Rough-chop into small, even pieces so the mixture stays cohesive when spooned onto crisps.
In a medium bowl, combine the chopped artichokes, tomatoes, garlic, olive oil, lemon juice, salt, and pepper. Mix gently until everything is evenly coated.
Let the mixture rest for about 10 minutes so the flavors meld. Spoon onto Parmesan crisps just before serving and finish with a very light drizzle of balsamic vinegar, if desired.
Parmesan Crisps (Low-Carb Base):
Preheat the oven to 400°F and line a baking sheet with parchment paper. Spoon about 1 tablespoon of Parmesan per crisp onto the sheet and flatten slightly. Bake for 5–7 minutes, until melted and golden. Let cool for 2 minutes — they will crisp up as they cool.