In a 12 inch to 14 inch saute pan, heat oil and garlic together until garlic starts to lightly brown. Add all the cavolo at once and stir to move garlic from the bottom. Cover and cook 8 to 10 minutes until cavolo is soft.
Meanwhile, grill the bread and then rub with raw garlic. Place 1 slice in each shallow bowl and top with a large spoonful of the cabbage. Drizzle with 1 tablespoons extra virgin olive oil and shaved pecorino from a peeler.