Drain the red peppers, reserving 2 tablespoons of the brine. Slice the peppers thinly. Combine the reserved brine with the oil, vinegar, and a big pinch of salt and pepper.
In a salad bowl, toss the salad mix with the peppers, lima beans, and dressing. Add the almonds. Using a vegetable peeler, shave on the cheese. Season to taste with salt and pepper.