Preheat oven to 325°F (163°C). Grease and flour a large bundt or tube pan.
In a large bowl, cream butter and shortening until light and fluffy. Gradually add sugar, beating until creamy.
Beat in eggs one at a time, mixing well after each addition.
In a separate bowl, sift together flour, baking powder, and salt.
Add flour mixture to the creamed mixture in three additions, alternating with buttermilk. Begin and end with flour. Stir in vanilla.
Gently fold in strawberries, coconut, and pecans. Avoid overmixing.
Pour batter into the prepared pan and smooth the top. Bake for 1 hour and 10–15 minutes, or until a toothpick comes out clean.
Cool cake in the pan for 15 minutes, then transfer to a wire rack to cool completely.
To make the frosting, beat cream cheese and butter until smooth. Add powdered sugar gradually, then mix in mashed strawberries, vanilla, and a pinch of salt.
Spread or pipe frosting over the cooled cake. Garnish with extra strawberries or chopped pecans if desired.