1. Preheat oven to 350°F. Toss artichokes with crushed red pepper, garlic and 2 Tbsp. olive oil; season with salt and pepper. Place in a single layer on a large baking sheet and bake until garlic is golden and edges of artichokes begin to brown, 20 to 25 minutes, stirring occasionally. Cool slightly.
2. Bring a pot of salted water to a boil. Cook pasta until just tender, about 8 minutes. Rinse under cold water; drain. Transfer to a serving bowl. Toss with tomatoes, onion, olives and artichokes.
3. In a bowl, roughly mash capers with a fork. Stir in vinegar, mustard and lemon zest and juice. Measure 2 Tbsp. oil from sun-dried tomatoes; add to remaining olive oil. Slowly pour oil into vinegar mixture, whisking. Pour over pasta mixture; toss. Stir in parsley. Season with salt and pepper. Serve at room temperature or chilled.