Preheat the broiler and position an oven rack about 6 inches below the heating element.
Pat the block of firm tofu dry with paper towels and slice into 1/2-inch-thick strips for fries.
Coat a baking sheet with cooking spray and arrange the tofu strips in a single layer; spray the tops lightly with cooking spray.
Broil the tofu for 7–10 minutes until the bottoms are browned, then carefully flip each strip and broil an additional 7 minutes or until all sides are browned and slightly crisp.
Season the hot tofu fries with salt and pepper to taste (optional) and set aside.
Drain the defrosted spinach thoroughly, squeezing out as much water as possible with your hands or a clean towel.
In a food processor, combine the light mayonnaise, grated Parmesan, silken tofu, garlic, lemon juice, and 1/2 teaspoon salt; blend until smooth and well combined.
Add the drained spinach and chopped fresh dill to the processor and pulse a few times until incorporated but still slightly textured.
Add the drained marinated artichoke hearts and pulse 3–4 times until the artichokes are coarsely chopped and evenly distributed through the dip.
Transfer the dip to a serving bowl and serve warm or at room temperature with the baked tofu fries and raw vegetables.