Place cauliflower, carrots, and asparagus into a large bowl. Drizzle with olive oil, season with salt and pepper, and toss to coat. Arrange in a single layer on a foil-lined baking sheet, separating the asparagus from the cauliflower and carrots.

Roast for 15 minutes, until asparagus is tender. Remove the asparagus and set aside. Return the baking pan to the oven for an additional 5 minutes, until the cauliflower and carrots are tender. Set aside.

While the cauliflower, carrots, and asparagus are roasting, add spinach and 1 tablespoon of water to a large skillet over medium-high heat. Cook, stirring frequently until spinach is wilted. Transfer the spinach to a colander, rinse with cold water, and squeeze out as much liquid as possible. Spread out on a kitchen towel to dry.

Reduce the oven temperature to 375°F.

Arrange the carrots and asparagus lengthwise to cover the pate. Top with cauliflower and spinach.

Carefully roll into a log shape so that the vegetables are completely covered by the puff pastry dough. Pinch the ends closed and tuck under. Lightly brush melted butter over the surface.