Bring a 4-quart / 4 L stockpot of well-salted water to a boil. Add the cauliflower florets and cook for 6 to 8 minutes, until a knife pierces the stem easily but the floret still holds its shape.
Drain the cauliflower in a colander and spread it on a tray to cool completely at room temperature. This stops the cooking and keeps the edges from going gray.
While the cauliflower cools, whisk the olive oil, red wine vinegar, crushed garlic clove, and black pepper in a small bowl. Set aside so the garlic can flavor the oil.
In a large mixing bowl, combine the cooled cauliflower, green olives, black olives, capers, chopped anchovies, pickled peppers, and giardiniera.
Remove the garlic clove from the dressing and pour the dressing over the salad. Toss gently with your hands or two spoons, taking care not to break up the cauliflower florets.
Cover the bowl and refrigerate for at least 4 hours, though overnight is better. Taste the next day and add a splash more vinegar or a few extra olives if the flavors need reinforcing.
Before serving, taste and adjust salt, keeping in mind the anchovies and capers are already salty. Arrange on a platter and top with quartered hard-boiled eggs.