Preheat oven to 375°F. Line a large baking sheet with foil. Pierce sweet potatoes all over with a fork, then coat with cooking spray. Place on the prepared baking sheet. Bake until a paring knife inserted into the center meets no resistance, about 45 minutes. Transfer to a plate and refrigerate, uncovered, until mostly cooled and slightly firm, about 45 minutes.

Meanwhile, melt 2 tablespoons butter in a medium saucepan over medium heat. Add ⅓ cup pecans; cook, stirring constantly, until lightly browned and fragrant, 2 to 3 minutes. Remove pan from heat and set aside to cool slightly.

Cut sweet potatoes in half lengthwise. Carefully scrape out cooked potato flesh, leaving shells with ¼ inch of flesh intact. Add flesh to the saucepan with the pecans. Arrange the potato skins, cut-sides up, on the baking sheet. Bake until the edges and outer skins are slightly crispy, about 10 minutes.

Meanwhile, cook sweet potato-pecan mixture over medium heat, stirring often, until smooth and most of the moisture has evaporated, about 5 minutes. Remove from heat; stir in 1 tablespoon maple syrup, ½ teaspoon each cinnamon and salt and ¼ teaspoon ginger until evenly combined. (You should have about 1½ cups.)

Spoon about ¼ cup sweet potato mixture into each baked potato skin; gently spread in an even layer. Top the sweet potatoes with ⅔ cup miniature marshmallows, gently pressing them into the sweet potato mixture.

Bake at 375°F until marshmallows are browned, about 12 minutes.