Preheat the oven to 375˚ F. Bake the potatoes in the center of the oven until tender but still firm in the center, 35 to 40 minutes. Let cool slightly, about 30 minutes. Cut each sweet potato lengthwise into 6 wedges and arrange cut-side up in a single layer on a baking sheet. Drizzle with olive oil (about 1/4 cup) and sprinkle with salt. Bake until crisp and browned around the edges, 25 to 30 minutes. Bring the brown sugar and 3/4 cup water to a simmer in a small saucepan. Stir in the pumpkin pie spice and cook over medium-low heat until syrupy, 3 to 5 minutes. Arrange the sweet potatoes on a platter and drizzle with the sauce.