Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Roll out the puff pastry on the prepared baking sheet and score a 1-inch border around the edges with a knife, being careful not to cut all the way through.
In a medium bowl, mix together ricotta, mozzarella, and Parmesan cheese with the minced garlic, half the thyme, and a pinch of salt and pepper.
Spread the cheese mixture evenly over the pastry, staying within the scored border.
In a large bowl, toss the sliced butternut squash, beets, and sweet potato with olive oil, remaining thyme, salt, and pepper.
Arrange the vegetable slices in an overlapping pattern over the cheese layer, creating a beautiful design (circles, rows, or whatever makes you happy!).
Brush the pastry border with beaten egg and drizzle the honey over the vegetables.
Bake for 40-45 minutes until the pastry is golden brown and puffed, and the vegetables are tender.
Let cool for 5 minutes, then top with fresh arugula before slicing and serving warm.