Preheat oven to 425°. Toss cauliflower florets with 3 tablespoons olive oil in a large bowl; season mixture with salt and pepper. Divide cauliflower mixture between 2 large rimmed baking sheets, spreading out in a single layer. Roast, tossing occasionally, until cauliflower is golden and crispy, about 45 minutes. DO AHEAD: Cauliflower can be made 4 hours ahead. Let stand at room temperature. Reheat before using.

Meanwhile, heat remaining 3 Tbsp. olive oil in a small saucepan over medium-low heat. Add garlic and cook, stirring occasionally, until just golden, 5–6 minutes. Add capers and cook until they start to pop, about 3 minutes longer. Add breadcrumbs and toss to coat. Cook, stirring often, until breadcrumbs are golden, 2–3 minutes; transfer breadcrumb mixture to a plate and set aside.

Add chicken broth and anchovy paste (if using) to same saucepan. Bring to a boil. Add golden raisins and white wine vinegar and cook until almost all liquid is absorbed, about 5 minutes. Remove from heat and set aside. Do ahead: Breadcrumb and raisin mixtures can be made 2 hours ahead. Rewarm raisin mixture mixture before continuing.

Transfer warm cauliflower to a serving bowl. Scatter raisin mixture over, then toss to distribute evenly. Season to taste with salt and pepper. Sprinkle cauliflower with breadcrumb mixture and parsley.