Preheat oven to 350°F and line your mini loaf pans with parchment paper or lightly grease them to prevent sticking.
In a large bowl, whisk together the flour, salt, and baking powder until evenly combined. This helps distribute the leavening so the loaves bake evenly.
In a separate bowl, add the almond milk, applesauce, melted dairy-free butter, white sugar, and brown sugar. Whisk until the mixture is smooth and fully combined, with no streaks of butter remaining.
Pour the wet ingredients into the dry ingredients. Using a spatula or spoon, gently mix until just combined and no dry streaks remain. Be careful not to overmix, as this can make the loaves dense instead of soft.
Add the cranberries, orange zest, and orange juice. Fold them into the batter until evenly distributed throughout. The batter will be thick.
Divide the batter evenly between the prepared mini loaf pans and spread the tops smooth. Lightly tap the pans on the counter to release any air bubbles.
Bake for 25–30 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the loaves cool in the pans for about 10–15 minutes, then carefully remove and transfer to a wire rack to cool completely before slicing or serving.