Combine the parsley, 1/4 cup of the oil, vinegar, garlic, cumin, 1/4 teaspoon of the red pepper flakes and a large pinch of salt in a blender. Blend until mostly smooth, slowly adding olive oil of necessary to reach the desired consistency. Season with additional salt if needed. Set the chimichurri aside.
Heat a large high-sided skillet over medium-high heat. When the skillet is hot, add the remaining 1 tablespoon oil and swirl to coat the pan. Add the chorizo and cook until lightly browned and cooked through, about 5 minutes, breaking up the meat with a rubber spatula or wooden spoon. Add the onion and a large pinch of salt and cook until softened, 2 to 3 minutes, stirring frequently.
Add the stock, lemon juice, lime juice, 2 tablespoons of the chimichurri, the butter and remaining 1/4 teaspoon red pepper flakes. Cook, stirring occasionally, until the butter is melted and the stock is simmering, 2 to 3 minutes. Add the clams and cover with a tightly fitting lid. Cook until the clams have opened, about 5 minutes.
Meanwhile, heat a cast-iron grill pan over medium-high heat. Spread half of the remaining chimichurri on 1 side of each of the 4 slices of bread. Place the bread slices on the pan and grill until crispy and charred in spots, about 2 minutes. Flip and grill until charred in spots on the other side, about 1 minute. Transfer the bread to a plate.
To serve, spoon the clams and broth into 2 large serving bowls (discard any clams that do not open). Drizzle with the remaining chimichurri and serve with the grilled bread.