Bring a large pot of salted water to a boil. Have a large ice bath ready.
Add the broccoli, cauliflower and artichokes to the boiling water and cook until crisp tender, 2 to 3 minutes. Drain and transfer to the ice bath to stop the cooking. Drain the vegetables and pat dry with paper towels.
Whisk together the olive oil, vinegar, garlic and 3/4 teaspoon salt in a large bowl. Add the broccoli, cauliflower, artichokes, olives, capers, oregano and cherry peppers and toss to coat. Cover and refrigerate at least 2 hours and up to overnight. Serve cold or at room temperature.