Place the cauliflower, carrots, onion, and oregano in a shallow heat-proof glass or nonreactive bowl. Bring the sugar, salt, vinegar, and water to a boil in a small pot, stirring until the sugar and salt are dissolved. Pour the hot brine over the vegetables, stir to combine and cover with plastic wrap. Let the vegetables stand, stirring occasionally, 30 minutes. Serve at room temperature or place in the refrigerator and chill for 1 hour or up to 2 days.
To make the Grilled Peppers:
Preheat a grill, broiler or oven on high heat. Grill, broil or roast the peppers until the skin is black and blistered. Place in a small bowl and cover with plastic wrap. Let stand about 15 minutes, or until cool enough to handle, but still warm. Rub the skin off the peppers, then seed and cut into about 1-inch slices. Place in a jam jar or small container and season with salt and pepper. Add the garlic and pour in the olive oil until peppers are completely covered. Let stand about 30 minutes and serve at room temperature or place in the refrigerator for up to 2 weeks, keep covered with oil.
To make the olives:
Mix the olives, parsley, garlic, basil, oregano, lemon zest, red pepper flakes, and olive oil in a bowl and let the olives marinate for 30 minutes before serving.