Press and Slice the Tofu: Press for at least 15 minutes. Slice into eight ¼-inch (0.6 cm) medallions.
Marinate the Tofu: Whisk 1 tbsp olive oil, lemon juice, garlic, oregano, and ⅛ tsp fine sea salt. Coat tofu, cover, and refrigerate for at least 30 minutes.
Prepare the Vinaigrette: Blend cannellini beans, 2 tbsp white balsamic vinegar, 2 tbsp olive oil, 1 tbsp water, 1 tsp Dijon, and ⅛ tsp fine sea salt until creamy (30–45 seconds).
Build the Salad Base: Thinly slice cucumber. Spread arugula on a large platter and arrange cucumber over it.
Assemble the Salad: Slice tomatoes into ¼-inch (0.6 cm) rounds. Alternate tomato slices and marinated tofu over the greens.
Dress and Garnish: Drizzle vinaigrette, tuck in basil, finish with black pepper, and serve immediately.