Melt the butter in a large skillet over medium heat. Add the diced apple, dark brown sugar, cinnamon, nutmeg and salt. Cook, stirring frequently, until the apples are tender but still hold their shape and the released liquid has reduced completely. The apples should look moist and coated with the brown sugar mixture, with no syrup remaining in the skillet.
1 tsp (2.5 g) unsalted butter, 1¼ cups (150 g) Honeycrisp or Pink Lady apple, 2 tbsps (25 g) dark brown sugar, 1 tsp (2.5 g) ground cinnamon, ¼ tsp (0.5 g) freshly grated nutmeg, pinch kosher salt
Remove the skillet from the heat, then stir in the vanilla extract. Transfer the apple mixture to a shallow plate and spread it out to cool. Once completely cool, refrigerate until thoroughly chilled.
1 tsp (5 ml) vanilla extract
Meanwhile, whisk together the flour, cream of tartar, baking soda, salt and cinnamon in a medium bowl. Set aside.
3 cups (375 g) all-purpose flour, 2 tsps (6 g) cream of tartar, 1 tsp (4.6 g) baking soda, ½ tsp (1.5 g) kosher salt, 1½ tsps (4 g) ground cinnamon
In a large mixing bowl, beat the softened butter, granulated sugar and light brown sugar with a stand mixer or electric hand mixer until light and fluffy, 2–3 minutes.
1 cup (226 g) unsalted butter, ¾ cup + 2 tbsps (170 g) granulated sugar, ⅓ cup (75 g) packed light brown sugar
Add the egg and beat until incorporated. Add the egg yolk and mix until combined, then mix in the vanilla extract.
1 large egg, 1 large egg yolk, 2 tsps (10 ml) vanilla extract
Gradually add the dry ingredients and mix on low speed until the cookie dough is almost combined, stopping while a few streaks of flour are still visible.
Using a rubber spatula, fold the thoroughly chilled apple mixture into the dough about 5–8 times. Stop once the remaining flour is incorporated and the apples are irregularly distributed throughout the dough rather than continuing to mix until the dough looks uniform.
Cover the dough and refrigerate for 1 hour.
When ready to bake, preheat the oven to 375°F (190°C) and line baking sheets with parchment paper.
Meanwhile, combine the granulated sugar and cinnamon for the coating in a shallow bowl.
¼ cup (50 g) granulated sugar, 1 tbsp (8 g) ground cinnamon
Portion the chilled dough into 55-gram portions, about 3 tablespoons each. Shape each portion into a ball without tightly compressing the dough, then coat generously with the cinnamon-sugar mixture.
Arrange the cookie dough balls about 3 inches (7.5 cm) apart on the prepared baking sheets.
Bake for 10–12 minutes, beginning to check at 10 minutes. The cookies are ready when the outside looks set and lightly golden while the centers remain soft and slightly puffed. Do not wait for the centers to appear completely set.
Finally, allow the cookies to cool on the baking sheets for 10 minutes so the centers can continue setting from the heat of the pan. Transfer to a wire rack and cool completely.