Combine the cilantro, parsley, oregano, shallot, garlic, and jalapeño in a food processor. Add the lemon juice, red wine vinegar, extra virgin olive oil, kosher salt, and a few grinds of black pepper. Pulse until finely chopped and well combined. Set aside.
Season the chicken thighs with the kosher salt, black pepper, and smoked paprika, pressing the spices onto the chicken. Spoon 1/4 cup of the chimichurri over the chicken and toss to coat. Let marinate for at least 15-20 minutes while preparing the remaining ingredients.
Meanwhile, combine the rice and chicken broth or water in a medium saucepan. Bring to a boil, cover, reduce the heat to low, and cook for 15 minutes, or until the liquid is absorbed. Remove from the heat and let stand for 5 minutes before fluffing with a fork.
Heat the extra virgin olive oil in a large skillet set over medium-high heat. Add the chicken and cook for 5-6 minutes per side, until deeply golden and cooked through to 165 degrees F. Transfer to a cutting board and rest for 5 minutes before slicing.
Add the bell pepper, poblano pepper, and zucchini to the skillet. Cook for 5-7 minutes, stirring occasionally, until tender-crisp and lightly charred around the edges.
Divide the rice among serving bowls. Top with the sliced chicken, sautéed vegetables, and shallot slices. Spoon the remaining chimichurri over the bowls. Garnish with fresh cilantro leaves before serving.