Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats to prevent sticking and promote even baking.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and fine sea salt until well combined. Set aside.
2 1/4 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon fine sea salt
In a large mixing bowl, using a hand mixer or a stand mixer fitted with the paddle attachment, beat the softened butter, neutral oil, and granulated sugar on medium speed for 2–3 minutes, or until light and fluffy.
1/2 cup unsalted butter, 1/2 cup neutral oil, 1 cup granulated sugar
Beat in the eggs one at a time, mixing well after each addition and scraping down the sides of the bowl as needed. Add the vanilla extract, sour cream or Greek yogurt, orange zest, and orange juice. Mix until fully combined; the mixture may look slightly curdled, which is fine.
2 large eggs, 2 tablespoons sour cream or plain Greek yogurt, 1 1/2 teaspoons vanilla extract, 2 tablespoons orange zest, 3 tablespoons orange juice
Add the flour mixture to the wet ingredients in two additions, mixing on low speed just until no dry flour streaks remain. The dough should be soft and slightly sticky, similar to thick cake batter. If it seems very loose, let it rest for 5 minutes so the flour can absorb some moisture.
2 1/4 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon fine sea salt
Using a small cookie scoop (about 1 1/2 tablespoons) or a rounded tablespoon, drop mounds of dough onto the prepared baking sheets, spacing them about 2 inches apart to allow for spreading.
Bake the cookies for 9–11 minutes, rotating the pans halfway through baking if your oven has hot spots. The cookies should be set around the edges and pale on top without browning. Remove from the oven before they turn golden to keep them soft.
Allow the cookies to cool on the baking sheet for 3–4 minutes, then transfer them carefully to a wire rack to cool completely. Do not glaze warm cookies or the glaze will run off.
In a medium bowl, whisk together the powdered sugar, 3 tablespoons of fresh orange juice, orange zest, vanilla extract, melted butter (if using), and a pinch of salt until smooth. If the glaze is too thick, add more orange juice 1/2 teaspoon at a time; if it is too thin, add a bit more powdered sugar. Aim for a thick but pourable glaze that ribbons off the spoon.
2 cups powdered sugar, 3-4 tablespoons orange juice, 1-2 teaspoons orange zest, 1 teaspoon vanilla extract, 1-2 teaspoons melted butter, 1 pinch salt
Once the cookies are completely cool, spoon or drizzle the orange glaze over the tops, letting it drip slightly down the sides. For a smoother, more polished finish, dip the tops of each cookie into the glaze, then let the excess drip off before placing them back on the wire rack.
Allow the glazed cookies to sit at room temperature for 30–45 minutes, or until the glaze is set and dry to the touch. Once set, stack, store, or serve as desired.