Preheat oven to 425ºF.Prepare wild rice blend according to package instructions in salted water until tender. Set aside.

Toss sweet potatoes in 1 to 2 Tbsp. olive oil, ½ tsp. salt, and ¼ tsp. black pepper on a large rimmed baking sheet. Roast for 20 minutes, tossing once halfway through.Toss sweet potatoes and add Brussels sprouts to baking sheet. Drizzle with 2 Tbsp. olive oil and remaining ½ tsp. salt and ¼ tsp. black pepper; toss to coat. Roast for 10 more minutes.

Meanwhile, prepare Caramelized Shallot Dressing: heat 2 Tbsp. olive oil in a small or medium skillet over medium heat. Add sliced shallots and sauté for 2 minutes. Slightly reduce heat and continue cooking until shallots are nicely caramelized, about 6 more minutes. Stir in garlic during final minute. Remove pan from heat and allow to slightly cool.

Transfer caramelized shallots, garlic, and residual cooking oil to a small blender or container for immersion blending. Add remaining 3 Tbsp. olive oil, sherry vinegar, Dijon mustard, honey, rosemary, salt, and pepper; blend until smooth. (If the dressing needs thinning, add an extra 1 Tablespoon of olive oil.)

Assemble salad by combining cooked wild rice, roasted sweet potatoes and Brussels sprouts, shredded chicken, pecans, and pomegranate arils in a large bowl. Add dressing and toss to combine. Serve warm or closer to room temperature.