Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.

Place butternut squash halves on the prepared baking sheet, flesh side up.

Roast in the preheated oven until squash is fork tender and easily pierced with a knife, 45 to 50 minutes.

Meanwhile, heat oil in a skillet over medium heat; add carrot, onion, and garlic and sauté until fragrant, 3 to 5 minutes. Remove from heat.

Remove squash from the oven and cool until easily handled. Scoop cooked squash into a bowl; discard skins.

Combine chicken broth, 1/2 cup evaporated milk, half-and-half, sautéed veggie mixture, cooked squash, cayenne pepper, salt, and pepper in a high-performance blender (such as Vitamix®) in the order listed. Blend for 5 minutes 45 seconds, then turn down to variable speed 1.