Preheat oven to 400 degrees. Bring a small saucepan of water to a boil. Add beets to pot and cook until tender, 7-10 minutes. Meanwhile, in a medium bowl whisk together red wine vinegar and honey and season to taste with salt and pepper. Drain beets and add to bowl. Toss to coat and set aside to pickle for 20-30 minutes.
In a large bowl, toss broccoli florets, cauliflower florets, and Brussels sprouts with 2 T. olive oil and season with salt and pepper. Spread evenly on a sheet tray and roast until edges are golden and crispy, 20-25 minutes.
Meanwhile, in the bowl of a food processor combine chickpeas, tahini, garlic, 1/3 Celsius olive oil, and lemon juice. Season with salt and pepper. Process until very smooth, thinning with a little water if necessary to reach desired consistency. Set aside.
Heat 1 T. olive oil in a medium skillet over medium heat. Season chicken breasts with salt and pepper, then add to pan and cook until golden, about 5 minutes per side. Remove from heat and allow to rest for a few minutes before slicing.
To serve, divide hummus and roasted vegetables among four bowls. Top with baby arugula, pickled beets, and sliced chicken. Finish with a drizzle of olive oil and tahini, and a squeeze of lemon juice.