In a large mixing bowl, use a handheld mixer to combine butter and sugars until creamy. Beat in the non-dairy milk and vanilla extract until combined.

Add flour, oats, baking soda, and salt. Combine on low speed until a soft cookie dough forms. Refrigerate dough for at least 1 hour (this is crucial to maintain cookie shape and reduce spread).

Preheat oven to 350°F. Use a 2 tbsp cookie scoop to portion out dough on to a lined baking sheet, about four to a sheet. Slightly press cookie dough down. These cookies will spread quite a bit, but that's what creates a soft and chewy texture. Bake for 10 minutes until golden brown and crisp on the edges. They may appear slightly underdone in the middle - that's ok! It will set once cooled.

Cool cookies for 10 minutes on the baking sheet before transferring to a wire cooling rack. Allow cookies to completely cool.

In a medium saucepan, stir together the diced strawberries, cherries, and sugar. Cook over medium heat, stirring occasionally, until fruit becomes soft and breaks down, about 4-5 minutes.

Strain the mixture through a fine mesh colander, reserving the juices. Use the solids to make a fruit spread, top on pancakes/waffles, or oatmeal - don't let that yummy fruit go to waste.

In a large mixing bowl, use a handheld mixer to cream the cream cheese, butter, vanilla extract, and salt until light and fluffy, about 2 minutes. Add the powdered sugar 1 cup at a time, mixing each until combined. Add all of the reserved fruit juice, mixing it into the filling on low speed. If the filling seems a bit thin, you can add a touch more powdered sugar to thicken. It should have the consistency of marshmallow fluff, spread easily, and not melt off the sides of the cookie.

Flip over half the cooled cookies and use an offset spatula or spoon to spread the filling on top of the flipped cookies. Press the remaining cookies on top to make sandwiches. Refrigerate the cookies in an airtight container for up to 5 days.