Season pork with salt and pepper. In a large straight-sided skillet, heat 1 teaspoon oil over medium-high. Add pork and cook until browned on both sides, about 7 minutes total. Whisk together broth, flour, and 1/2 teaspoon chili powder and add to skillet. Bring liquid to a boil; reduce to a rapid simmer, cover, and cook 30 minutes. Uncover and cook until pork is tender and sauce is thickened, about 20 minutes.
Meanwhile, in a medium pot, bring sweet potatoes to a boil in salted water over high. Reduce to a rapid simmer and cook until tender when pierced with a knife, 20 minutes. Drain potatoes and return to pot; mash until fluffy and almost smooth. Stir in sour cream and sugar, season with salt and pepper, and keep warm over low heat.
In a large skillet, heat 2 teaspoons oil over medium-high. Add garlic and cook until fragrant, 30 seconds. Add green beans and 1/4 cup water, cover, and cook 3 minutes. Uncover and cook, stirring occasionally, until crisp-tender and water is evaporated, 2 minutes. Season with salt and pepper and serve with pork, sauce, and sweet potatoes sprinkled with chili powder.