Preheat the oven to 425°F. Line a large baking sheet with parchment paper or lightly grease it.
In a large bowl, whisk together the mayonnaise, soy sauce, olive oil, garlic powder, black pepper, cayenne, and salt until smooth.
Add the chicken to the bowl and toss until every piece is fully coated. Transfer the chicken to the baking sheet.
Add the halved potatoes to the same bowl with the remaining marinade. Sprinkle with the extra 1/2 tsp salt and toss to coat. Nestle the potatoes between the chicken pieces on the pan. Reserve the bowl for the broccoli.
Bake for 30 to 35 minutes until the chicken starts to brown and the potatoes begin to soften.
Remove the pan from the oven. Add the broccoli to the reserved bowl and toss with any remaining marinade, the extra garlic powder, and a pinch of salt. Flip the chicken pieces, then nestle the broccoli between the chicken and potatoes.
Return to the oven and bake for another 10 to 15 minutes until the chicken reaches 165°F, the potatoes are fork-tender, and the broccoli is lightly crisped at the edges.