In a food processor, combine the fresh flat-leaf parsley, cilantro, fresh oregano, minced red onion, and minced garlic cloves. Pulse until the herbs are roughly chopped and the mixture is fragrant, about 2-3 pulses. Add the red chili flakes and ground cumin, then pulse once more to distribute the spices evenly. Pour in the extra virgin olive oil, red wine vinegar, and fresh lemon juice, then pulse 2-3 more times until everything is well combined but still has some texture—the sauce should be vibrant green and slightly chunky, not a smooth paste. Finally, stir in the kosher salt by hand and taste for seasoning, adjusting as needed. Set the chimichurri aside in a bowl; it will develop more flavor as it sits.
Pat all the vegetables dry with paper towels—this helps them char better on the grill. Arrange the portabella mushroom strips, eggplant rounds, zucchini planks, yellow squash rounds, red onion wedges, asparagus bunches, and red bell pepper pieces on a large cutting board or baking sheet. Drizzle the 3 tablespoons of olive oil over all the vegetables, then sprinkle with the smoked paprika, coarse kosher salt, and freshly ground black pepper. Toss gently to coat everything evenly, making sure all pieces are lightly oiled and seasoned. I like to season the vegetables generously because the grill will intensify the flavors, and the oil helps create those beautiful char marks.
Preheat your grill to medium-high heat (around 400-450°F) for 10 minutes. Working in batches so you don't overcrowd the grill, place the vegetables directly on the grates. Grill portabella mushrooms and eggplant for 3-4 minutes per side until they have good char marks and are tender. Grill zucchini, yellow squash, and bell pepper for 2-3 minutes per side. Asparagus needs only 1-2 minutes per side, and red onion wedges take about 3-4 minutes per side. Each vegetable cooks at a different rate, so keep an eye on them and move pieces around if needed to ensure even cooking and charring. Transfer grilled vegetables to a large platter as they finish.
Arrange all the grilled vegetables on a serving platter. Drizzle the chimichurri sauce generously over the warm vegetables, or serve it on the side for guests to add as much or as little as they like. I find that letting the vegetables stay warm while you drizzle the chimichurri helps the flavors meld beautifully. The heat from the vegetables will warm the sauce slightly, releasing even more of the fresh herb aromas. Serve immediately while the vegetables are still warm and the charred edges are at their best.