Wrap the venison loin tightly in plastic wrap and freeze for about 1 hour, until it is firm enough to slice thinly.
Using a sharp knife, slice the venison as thinly as possible. Arrange the slices on a chilled serving plate.
In a small bowl, whisk together olive oil, lemon juice, salt, and black pepper to make a light dressing.
Drizzle the dressing evenly over the venison slices. Sprinkle with capers and fresh thyme leaves.
Garnish with fresh arugula and shaved Parmesan cheese. Serve immediately with crusty bread or crackers on the side.
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