Preheat oven to 400 F (200 C). On parchment paper- or silicone mat-lined baking sheet, place chicken and season with salt and pepper. Place in oven and heat for 25 minutes, or until chicken is cooked to an internal temperature of 165 F (74 C). When cool enough to handle, slice chicken. Alternatively, you can prepare chicken on an outdoor grill.
Cut off broccoli florets as close as possible to the dark green flowers and roughly chop; add to large bowl. Trim woody ends from broccoli stems, preserving as much stem as possible. With sharp knife, peel thick skin of stems to expose tender inner cores. Thinly slice stems and add to bowl with florets. Add kale to bowl and toss to combine.
In small bowl, whisk together mayonnaise, vinegar, Parmesan, mustard, garlic, anchovies (if using), salt, and black pepper. In slow stream, whisk in olive oil. Add dressing to bowl with broccoli and kale, and toss until everything is well coated. With your hand, massage dressing into vegetables.
In small bowl, combine honey, red pepper flakes, lemon zest, and 1 Tbsp (15 mL) water. In dry medium-sized skillet over medium heat, toast sunflower seeds, pumpkin seeds, and sesame seeds, stirring often, until sesame seeds are lightly browned, about 3 minutes. Add honey mixture and cook, stirring often, until seeds stick together in small clumps and they look glazed, about 2 minutes. Scrape seed mixture onto parchment paper; let cool to harden together. Break into small clusters.
To serve, divide vegetables among serving plates and top with chicken slices and seed clusters. Garnish with shaved Parmesan.
Dressed greens, cooked chicken, and seed clusters can be stored separately in refrigerator for up to 3 days. Combine just before serving.