Prep the pan and oven: Heat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
Lightly mist liners with cooking spray for easy release.
Mix dry ingredients: In a medium bowl, whisk 1 1/2 cups flour, 1 1/2 teaspoons baking powder, and 1/2 teaspoon salt. Set aside.
Cream butter and sugar: In a large bowl, beat 1/2 cup softened butter with 3/4 cup sugar until light and fluffy, about 2–3 minutes.
Add oil and eggs: Beat in 1/4 cup neutral oil. Add 2 large eggs one at a time, mixing until just combined.
Stir in 1 teaspoon vanilla.
Add orange flavor: Mix in 1 tablespoon fresh orange zest and 1/3 cup fresh orange juice. If using, add 1/4 teaspoon orange extract.
Alternate dry and milk: On low speed, add half the dry ingredients, then 1/3 cup milk (or buttermilk), then the remaining dry ingredients. Mix just until combined.
Do not overmix.
Fill and bake: Divide batter evenly among liners, about two-thirds full. Bake 16–20 minutes, until tops spring back and a toothpick comes out clean or with a few moist crumbs.
Cool: Let cupcakes rest in the pan 5 minutes, then transfer to a wire rack to cool completely before frosting.
Make the frosting: Beat 6 ounces cream cheese and 1/4 cup unsalted butter until smooth. Add 2 cups powdered sugar, 1 tablespoon orange zest, 1–2 tablespoons orange juice, and a pinch of salt.
Beat until creamy and spreadable. Adjust with more sugar for thickness or a splash of juice for looseness.
Frost and garnish: Spread or pipe frosting onto cooled cupcakes. Garnish with extra zest, thin orange slices, or a sprinkle of sanding sugar if you like.