Preheat the oven to 450 degrees F. Pierce the sweet potatoes all over with a fork and microwave on a microwave-safe plate until tender, 20 to 25 minutes.
Meanwhile, heat 2 tablespoons olive oil in a small skillet over medium-high heat. Add the pickling spice and cook, stirring, until toasted, about 1 minute. Transfer the spiced oil to a mini food processor and pulse until the pickling spice is finely ground, about 1 minute. Transfer the spiced oil to a medium bowl and stir in the yogurt, garlic, 1 teaspoon salt and a few grinds of pepper; set aside.
Soak the raisins in 1/2 cup warm water in a small bowl, 10 minutes. Meanwhile, heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the chorizo and cook, stirring and breaking up the meat with a wooden spoon, until browned and crisp, 5 to 6 minutes. Stir in the pine nuts and cook, stirring, until lightly toasted, about 30 seconds. Transfer the chorizo mixture to a bowl. Drain the raisins and stir into the chorizo mixture.
Arrange the sweet potatoes on a foil-lined baking sheet. Drizzle with the remaining 1 tablespoon olive oil and season with salt and pepper; rub to coat evenly. Roast until the potato skins are crisp, about 10 minutes. Split open the sweet potatoes and fluff the flesh with a fork; season with salt and pepper. Top with the chorizo, yogurt sauce and mint.