Whisk vinegar, honey, and ¾ teaspoon salt together in medium bowl. Add cauliflower and stir to coat. Microwave until simmering, 1½ to 2 minutes. Stir, then cover and let sit, stirring occasionally, until cauliflower is crisp-tender, about 5 minutes. Using slotted spoon, transfer cauliflower to small plate, leaving liquid in bowl.
Heat ½ teaspoon oil in 8-inch nonstick skillet over medium-high heat until shimmering. Add halloumi and cook until brown on both sides, 60 to 90 seconds per side. Remove from heat and cover to keep warm.
Transfer 2 tablespoons pickling liquid to large bowl. Add remaining 2 tablespoons oil and whisk to combine. Add lettuce and radicchio, season with salt and pepper to taste, and toss to combine. Distribute greens evenly between 2 shallow serving bowls. Place chickpeas in now-empty bowl.
Add yogurt, tahini, garlic, Aleppo pepper, and remaining ¼ teaspoon salt to remaining pickling liquid and whisk until combined. Add ¼ cup yogurt mixture to chickpeas and toss to combine. Arrange cauliflower, halloumi, and grapes in piles atop greens. Drizzle remaining yogurt mixture over cauliflower, grapes, and halloumi in each bowl. Divide chickpea mixture evenly between bowls and serve.
