Adjust oven rack to upper-middle position and preheat oven to 400°F (200°C). Spray a 12-cup muffin pan generously with vegetable oil spray.
In a 12-inch (30-cm) skillet over medium-high heat, melt 2 tablespoons butter. Add apples, brown sugar, and 1/4 teaspoon cinnamon. Cook, stirring often, until the moisture has completely evaporated and the apples are well browned, about 9 minutes. Remove skillet from heat and let cool for 10 minutes.
Meanwhile, in a large bowl, whisk flour, baking powder, baking soda, salt, and remaining 1/2 teaspoon cinnamon together.
In a separate bowl, whisk granulated sugar, eggs, oil, and 4 tablespoons melted butter together until thick and homogeneous, about 30 seconds. Whisk cider, yogurt, and vanilla into sugar mixture until combined.
Fold sugar mixture and cooled apples into flour mixture until just combined. Using greased 1/3 cup dry measuring cup, divide batter evenly among prepared muffin cups (cups will be filled to rim); sprinkle muffin tops evenly with topping.
Bake until golden brown and toothpick inserted in center comes out with few crumbs attached, 18 to 22 minutes, rotating muffin pan halfway through baking.
Let muffins cool in muffin pan on a wire rack for 10 minutes. Remove muffins from muffin pan and let cool on wire rack 5 minutes. Serve. (Muffins can be stored at room temperature for up to 3 days.)