Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper and set aside.
In a medium bowl, whisk together 1 ½ cups all-purpose flour, ½ teaspoon salt, ½ teaspoon baking soda, and ½ teaspoon baking powder; set the dry mixture aside.
In a large bowl, use a hand mixer to beat ¾ cup room-temperature butter, ¼ cup shortening, 1 cup dark-brown sugar, and ½ cup granulated sugar until light and fluffy, about 1 to 2 minutes.
Add the 2 large eggs, 1 teaspoon vanilla, and ¼ teaspoon almond extract to the butter mixture and beat until incorporated.
With the mixer on low speed, add the flour mixture to the butter mixture and mix just until combined. Scrape down the sides of the bowl as needed.
Stir in 2 cups old fashioned rolled oats, 2 cups dried tart cherries, and 4 ounces chopped white chocolate or white chocolate chips with a spatula until evenly distributed.
Scoop about 2 tablespoons of dough per cookie onto the prepared baking sheets, leaving about 3 inches between cookies.
Bake one sheet at a time (or as oven space allows) for about 12 minutes, until the edges are just turning brown and the centers look slightly underdone.
Let the cookies cool on the baking sheet for about 2 minutes, then transfer them to a wire cooling rack to cool completely.