Preheat oven to 325°F (165°C) and grease and flour a loaf or bundt pan.
In a large bowl, beat softened butter and cream cheese until smooth and fluffy.
Add sugar and beat for 3 to 4 minutes until light and fluffy.
Beat in eggs one at a time, then mix in vanilla extract.
In another bowl, whisk together flour, baking powder, and salt.
Add dry ingredients to the batter alternately with milk, mixing just until combined.
Toss chopped strawberries with 1 tablespoon flour, then gently fold into the batter.
Pour the batter into the prepared pan and smooth the top.
Bake for 70 to 80 minutes (or 55 to 60 minutes for a loaf), until a toothpick inserted comes out clean.
Cool the cake for 15 minutes before removing from the pan.
For the optional glaze, whisk powdered sugar, strawberry puree or milk, and vanilla extract until smooth.
Drizzle the glaze over the cooled cake.
Slice and serve with coffee, tea, or fresh strawberries.