Spread your raw pumpkin seeds on a cookie sheet and roast for 8 minutes. Continue toasting if some are still green, until evenly brown but not burned. Check every few minutes until puffed and lightly brown. Shake a little salt on top and stir around, scrape onto a plate to cool.
Toss squash pieces and halved Brussels sprouts with about 1-2 tablespoons of olive oil on a rimmed cookie sheet. If vegetables look dry, add a little bit more oil to make sure they are lightly coated. Sprinkle with salt and pepper and cook for 20 minutes.
For the vinaigrette, add all ingredients to a small jar and shake well or whisk all ingredients in a small bowl. Set aside.
When your vegetables have cooked for 20 minutes, stir and check to see if squash and Brussels are tender by poking with a fork. If you prefer either vegetable to be cooked more, return to the oven for 5 minutes more at the most and taste to your liking.
To prep salad, toss kale pieces with a couple of tablespoons of dressing at a time, making sure that each piece gets coated. Give greens a good stir and see if you need more dressing. Add more as desired.
Spread your greens on a large serving platter or individual plates.
Top your plate of greens with warm squash, Brussels and chicken pieces. Sprinkle with 1/2 of your pumpkin seeds and grate pecorino cheese if using.
I like to leave extra dressing, cheese, and pumpkin seeds on the table so individuals can add more as desired.