Preheat the oven to 350°F (175°C). Line a 9x9 inch baking pan or a rimmed cookie sheet with parchment paper, or grease it well to prevent sticking.
Combine the undrained tuna (including the water), eggs, and flour in a bowl. If using an optional food processor, blend lightly to mix well. The mixture should be a thick, moist batter or soft dough consistency.
Spread the batter evenly into the prepared pan using a spatula. Sprinkle the top with Parmesan cheese, if desired.
Bake for about 20 minutes, or until the 'fudge' is firm to the touch but not overly crispy. Baking for longer will result in a crispier treat, while a shorter time yields a softer, fudge-like texture.
Cool completely, then use a pizza cutter or knife to cut into small, bite-sized training pieces.
Store in an air tight container in the refrigerator and use within 3 to 5 days.