Preheat the oven to 375 degrees F.
In a large saute pan set over medium-high heat, add the olive oil and chorizo. Cook until well browned, 7 to 8 minutes, breaking up the chorizo with the back of a wooden spoon as it cooks. Add the garlic, carrots, celery, shallots, salt, pepper and chile flakes, and saute until the onions become translucent, 5 to 6 minutes. Remove from the heat and transfer to a large mixing bowl to cool slightly. Add half of the Manchego, the breadcrumbs, half of the parsley and the cream cheese. Stir well to mix everything evenly. Using a medium spoon, carefully stuff each of the piquillo peppers with the filling. Arrange the stuffed peppers on a baking sheet and sprinkle with remaining Manchego. Bake in the center of the oven until the cheese melts and is slightly bubbly around the edges, 6 to 7 minutes. Transfer to a platter and garnish with the remaining chopped parsley to serve.