Heat the oil in a large heavy skillet with a lid over medium-high heat until it shimmers, then stir in the sweet potatoes and ½ to ¾ teaspoon of salt. Cover and cook, stirring occasionally and lowering the heat if the potatoes take on color too quickly. If the potatoes are browned but not yet soft, add ¼ cup water to the pan and cook until evaporated. Repeat as needed until the potatoes are tender, 12 to 15 minutes total.

Add the spinach, gently tossing until wilted, 2 to 3 minutes. Stir in the currants, pine nuts, and balsamic and season with salt to taste.