Toss the sliced Brussels sprouts and ancho chiles with the olive oil, 1 teaspoon salt and pepper, then spread out in 1 layer on a medium baking sheet. Roast until tender and golden brown, about 15 minutes. Remove from the oven and let cool 10 minutes.
Meanwhile, combine the mayonnaise, sour cream, honey and vinegar in a medium bowl. Season the dressing with salt and pepper. Toss the Brussels sprouts and ancho chiles with the dressing until well combined.
Refrigerate and serve cold.
Cook's Note: Use kitchen shears to easily snip the ancho chiles into rings.