In a large skillet, heat oil over medium-high. Add sweet potatoes; cook, stirring once, until beginning to brown, 2 minutes.
Add broth, packed brown sugar, and fresh lime juice; season with salt and pepper. Bring to a boil; reduce to a simmer, cover, and cook until crisp-tender, 10 minutes. Uncover, and cook over medium-high until sweet potatoes are tender and liquid is syrupy, 7 to 9 minutes more (there should be only a small amount of liquid remaining).
Remove skillet from heat; add butter, and swirl skillet until melted. Season with salt and pepper.