To add a variety of textures to these chicken tacos, we poach the chicken to keep it super-tender and moist while broiling the Brussels for a crisp mix-in. The creamy sauce rounds out the combo.
Place chicken in a large saucepan and cover with water by 1 inch. Bring to a simmer over high heat. Reduce heat to maintain a simmer and cook until an instant-read thermometer inserted in the thickest part registers 165°F, 12 to 15 minutes. Transfer to a clean cutting board to rest for 5 minutes.
Meanwhile, mix mayonnaise, lime juice and 1 teaspoon chile-lime seasoning in a small bowl. Toss Brussels sprouts with oil in a medium bowl. Spread on a rimmed baking sheet.
Position rack in upper third of oven; preheat broiler to high.
While the chicken rests, broil the Brussels sprouts until browned and tender, shaking the pan once halfway, 3 to 4 minutes.
Shred the chicken and toss with the remaining 1 teaspoon chile-lime seasoning. Serve in tortillas with the Brussels sprouts, sauce and cheese. Top with cilantro, onion and avocado and serve with lime wedges, if desired.