Giardiniera is an Italian pickled relish, and add tons of flavor to this frittata with broccoli and heirloom cherry tomatoes. Look for it with the pickles in your market.
Place a rack about 4 inches from the broiler and heat the broiler on high.
In a large bowl, toss the florets with 2 tsp. olive oil, ½ tsp. salt, and ¼ tsp. pepper. Place on a large rimmed baking sheet and broil, turning occasionally until browned and crisp on the edges, about 3 to 6 minutes.
Place a rack in the middle of the oven and heat the oven to 400°F.
Meanwhile, in a medium bowl, combine the eggs and ½ tsp. pepper.
Heat the remaining 2 Tbs. oil and butter in a 12-inch skillet over medium-high heat until the the butter melts. Add the giardiniera, stirring only once or twice, until some pieces are golden brown, using a splatter guard if necessary. Remove from the heat and add the broccoli, then gently pour in the egg mixture and redistribute the vegetables if necessary. Evenly distribute the ricotta in large dollops throughout the egg mixture, then scatter with the tomato slices and transfer to the oven. Bake until set, about 10 to 15 minutes; let rest for 5 minutes. Using a thin spatula, slide the frittata onto a serving dish, sprinkle with the basil, and cut into wedges.