Make the Dressing: In a small blender or a cup suitable for an immersion blender, combine all dressing ingredients: olive oil, lime juice, maple syrup, garlic, cilantro, smoked paprika, kosher salt, and cayenne. Blend until smooth and creamy. Set aside.
Prepare the Grill: Preheat your grill or grill pan over medium heat to approximately 375 ∘ F (190 ∘ C).
Season the Vegetables: In a large bowl, toss the zucchini, yellow squash, eggplant, red onion, and bell peppers with 2-3 tablespoons of the prepared dressing—just enough to lightly coat them. Season with the ½ teaspoon of black pepper.
Grill the Vegetables: Place the vegetables on the hot grill in a single layer, working in batches if needed. Grill for 8 to 10 minutes, flipping once, until they are tender and have clear char marks. Add the whole green onions to the grill during the last 3 minutes of cooking.
Chop and Combine: Remove the vegetables from the grill and let them cool for a minute on a cutting board. Coarsely chop everything into bite-sized pieces.
Assemble the Bowls: In a large bowl, toss the cooked farro with about half of the remaining dressing. Divide the farro among six bowls. Top with the grilled vegetable mixture, black beans, diced avocado, and crumbled cotija cheese. Drizzle the last of the dressing over the top, sprinkle with toasted pepitas, and serve immediately with fresh lime wedges.