Preheat oven to 425°F / 220°C.
Line a large sheet pan with parchment paper (or generously spray it with nonstick cooking spray). (Note: If all of the squash won't fit easily on one pan with some space, use two sheet pans.)
Toss butternut squash with 1 ½ Tablespoons olive oil and then brown sugar and salt. Spread out on prepared large sheet pan. Roast squash, without turning, until nearly tender, 15 minutes.
Remove squash from the oven and use a flat spatula to gently flip.
Continue roasting until squash can be easily pierced with a fork, 10 to 15 minutes more.
While squash roasts, heat a large skillet or griddle over medium-high heat. Cook bacon on both sides until very crisp, 6 to 10 minutes total. Transfer bacon to a paper towel-lined plate to cool slightly.
Combine all ingredients for the dressing and whisk well (or blend with an immersion blender for a very smooth dressing).
Just before serving, in a large salad bowl, toss together kale, Romaine, roasted butternut squash, bacon, and dried cranberries.
Add dressing and toss until dressed to your liking. Top with pepitas and cheese.