Preheat the oven to 400 degrees F.
Add the brussels sprouts, sweet potato, olive oil, garlic powder, cumin, allspice, and sea salt to a small casserole dish (8" x 8" or 9" x 13" will both work!). Toss everything together to coat the veggies.
Place on the center rack of the oven and bake 30 to 45 minutes, stirring once half-way through, or until veggies are golden-brown and cooked through.
In a small saucepan, heat the balsamic vinegar over medium-high and bring to a full boil. Cook at a full (but controlled) boil, stirring frequently, until vinegar is reduced by 1/2 of its original volume, about 5 minutes.
Taste veggies for flavor and add salt to taste. Serve roasted veggies with pecans, feta, and balsamic reduction drizzled on top.