Preheat the oven to 400°F (205°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, beat 1 cup unsalted butter (softened), ¾ cup brown sugar, and ½ cup granulated sugar with a hand mixer on medium speed until smooth and creamy, about 1 minute. The mixture should be pale and fluffy and visibly lighter in color.
Add 2 large eggs and 1 teaspoon vanilla extract. Mix on medium speed until just combined, about 30 seconds.
Add 1 cup cake flour, 1 ¾ cup all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, and ½ teaspoon salt. Mix on low speed until just combined. Do not overmix.
If using mix-ins (such as chocolate chips, chopped nuts, or dried fruit), fold them in by hand using a rubber spatula or large spoon until evenly distributed.
Divide the dough into 8–10 equal portions for large cookies (5-6 ounces each). Roll each portion into a ball with your hands and place them on the prepared baking sheets, spaced about 3 inches apart (4 per baking sheet).
Bake for 11 to 14 minutes, or until the tops are golden brown and edges are set.
Let cookies cool on the baking sheets for 15 minutes before serving warm. Alternatively, transfer to a wire rack to cool completely.