1. In a large nonreactive baking dish, combine 1/4 cup of the olive oil with the lemon juice and garlic. Season with salt and pepper. Add the chicken breasts and tenders, turn to coat and let marinate at room temperature for 1 hour, turning once.
2. Meanwhile, preheat the broiler. Broil the red peppers as close to the heat as possible, turning with tongs, until black all over. Transfer the peppers to a bowl, cover with plastic wrap and let cool. Peel, seed and core the peppers. Cut them into 3-by- 1/4 -inch strips.
3. Turn the oven to 425°. Arrange the salami or pancetta slices on a baking sheet and sprinkle with the Parmesan. Bake for about 10 minutes, or until browned. Transfer to paper towels to drain. When cool enough to handle, break the slices into 1-inch pieces.
4. In a medium bowl, combine the olives, shallot, capers, vinegar, mustard, salt and pepper. Stir in the remaining 6 tablespoons olive oil; don't worry if the dressing separates.
5. Heat a grill pan or cast-iron skillet over moderate heat. When the pan is hot, season the chicken with salt and pepper and grill or pan-fry until browned and crusty, about 4 minutes per side for the breasts and 3 minutes per side for the tenders. Let the chicken rest for 15 minutes, then slice crosswise 1/2 inch thick. Reserve any juices.
6. Just before serving, stir the parsley and any accumulated chicken juices into the dressing. In a large bowl, combine the spinach, radishes, roasted peppers and salami chips and toss with half of the dressing. Mound the salad on 4 large plates or a large platter and arrange the chicken on top. Spoon the remaining dressing over the chicken.
Make Ahead: All the elements can be refrigerated, covered, for up to 2 days.
Wine Recommendation: The sharp, lively flavors in this salad call for a straightforward dry white to cleanse the palate between bites. Consider a Rioja, such as the 1994 Marqués de Cáceres Blanco or the 1994 Bodegas Montecillo Cumbrero Blanco.