Prep Grapes: Cut the red grapes in half and set them aside for the chicken pan sauce.
Slice Shallots: Thinly slice the shallots for the chicken sauce. Keep them ready near the stove.
Season Chicken: Sprinkle both sides of the chicken breasts with kosher salt and black pepper.
Sear Chicken: Heat a large skillet over medium-high heat and add 1 tablespoon canola oil. Add the chicken breasts and sear for about 3 to 4 minutes per side, until golden brown.
Simmer Chicken: Pour the chicken broth into the skillet. Cover the pan and simmer over medium heat for about 6 to 8 minutes, until the chicken is cooked through.
Remove Chicken: Transfer the cooked chicken to serving plates or a clean plate. Let it rest while you make the sauce.
Start Pan Sauce: Add the unsalted butter to the skillet with the cooking liquid. Stir until the butter melts.
Add Vinegar and Fruit: Stir in 2 tablespoons red wine vinegar, the halved red grapes, and the sliced shallots. Cook for about 2 to 3 minutes, until the grapes soften slightly and the shallots begin to tenderize.
Add Olives and Herbs: Stir in the sliced Sicilian-style olives and fresh oregano leaves. Simmer the sauce for another 1 to 2 minutes, then spoon it over the chicken.
Prep Mushrooms: Remove the stems from the portabella mushrooms and scrape out the gills. Slice the mushrooms into thick strips.
Spray Mushrooms: Lightly coat the sliced mushrooms with nonstick cooking spray.
Cook Mushrooms: Wipe out the skillet or use a clean skillet. Heat it over medium-high heat, add the mushrooms, and cook for about 4 to 5 minutes, turning once, until browned and tender.
Make Dressing: In a mixing bowl, combine the minced garlic, minced shallot, remaining 2 tablespoons red wine vinegar, and remaining 2 tablespoons canola oil. Stir until mixed.
Toss Mushrooms: Pour the dressing into the skillet with the warm mushrooms. Stir for about 1 minute so the mushrooms soak up the dressing.
Plate Salad: Place the arugula leaves on the serving plates. Add the warm dressed mushrooms beside the chicken.
Finish with Cheese: Top the warm mushroom salad with shaved deli Manchego cheese. Serve with the chicken and grape-olive pan sauce.