Trim off the dry base of the sprouts and halve the heads. Using a sharp long knife finely shred them. Set aside in a large mixing bowl.
Wash kale leaves thoroughly under cold running water. Remove its tough center stems with a knife and discard them. Wrap the leaves tightly and shred thinly. Add to the brussels sprouts.
To make the dressing, whisk mustard, lemon juice and olive oil together. Season it with salt and freshly ground black pepper. Set aside.
Add pepitas to the hot skillet and let them brown on all side for about 3 minutes. Transfer seeds to a glass container and let cool.
Mix thinly shredded kale and brussels sprouts in a large bowl, add the dressing, cheese and seeds; toss to coat. Season to taste with salt and freshly ground black pepper.
