Chicken with Peruvian Chile Sauce

Chicken:

• Vegetable oil cooking spray
• 1 (4 to 5 pound) chicken, cut into 8 pieces
• 2 tablespoons vegetable oil
• Kosher salt and freshly ground black pepper

Sauce:

• 1 slice whole wheat sandwich bread, crust removed, cut or torn into 1/2-inch pieces
• 3/4 cup half-and-half
• 2 tablespoons vegetable oil
• 1 large or 2 small shallots, sliced
• 2 cloves garlic, crushed
• 1 cup low-sodium chicken broth
• 2 cups (6 ounces) crumbled queso fresco or mild feta cheese
• 1/2 cup finely grated Parmesan
• 1/2 cup chopped walnuts, plus 1/3 cup toasted (see Cook's Note)
• 1 tablespoon Aji Amarillo paste (found in Latin markets or the Hispanic section of grocery stores)
• 1/2 teaspoon turmeric
• 4 teaspoons kosher salt
• 1/2 tablespoon chopped fresh cilantro or flat-leaf parsley leaves