2Heat 1 tablespoon of the oil in a large frying pan over medium heat until shimmering. Add pecans, stir to coat in oil, and cook, stirring occasionally, until nuts are fragrant and golden brown, about 8 minutes. Remove from heat, add 1/2 teaspoon of the salt and 1/2 teaspoon of the smoked paprika, and stir to evenly coat the nuts. Add to the bowl with the reserved spinach.
3Return the pan to medium heat, add 1 tablespoon of the oil, and heat until shimmering. Add sweet potato, remaining 1 teaspoon salt, and remaining 1/2 teaspoon paprika and stir to coat the sweet potato. Cook, stirring occasionally, until sweet potato just gives way when pierced with a knife and is starting to brown at the edges, about 10 minutes. Add to the bowl with the nuts and spinach.
4Return the pan to medium heat, add remaining 2 tablespoons oil, and heat until shimmering. Add shallot and cook until just golden brown, about 1 minute. Remove from heat, add vinegar, brown sugar, and mustard and whisk to combine. Pour vinaigrette over spinach, nuts, and sweet potato and toss to coat. Serve immediately.