Make pizza the next day with the leftover meat and vegetables.
Preheat oven to 425 degrees. On 2 rimmed baking sheets, toss broccoli with 3 tablespoons oil and salt. Roast until tender and browned in spots, tossing, and rotating sheets once, 20 to 25 minutes.
Meanwhile, heat remaining 1 tablespoon oil in a large straight-sided skillet over medium-high heat. Cook sausage until browned on all sides, about 10 minutes. Remove and cut into 1/2-inch pieces.
Reduce heat to medium. Add garlic and pepper flakes; cook, stirring, 30 seconds. Add pickling liquid, broth, and beans; bring to a boil. Cook, mashing some beans with the back of a spoon, until slightly thickened, 5 minutes. Remove from heat; add pepperoncini. Reserve half of all for next day; serve remainder with polenta.