Preheat the oven to 350°F. Grease and flour a Bundt cake pan or spray with nonstick baking spray. In a large bowl, use an electric mixer on medium-high speed to beat together the cake mix, dry pudding mix, freeze dried strawberries, milk, oil, and eggs for about 2 minutes.
Pour the batter into the prepared pan; tap on the counter once or twice to release air bubbles.
Bake for 40 to 45 minutes, or until a toothpick inserted in the cake comes out clean. Cool for 10 minutes in the pan, then turn the cake onto a wire rack to cool completely before glazing.
In a small bowl, whisk together the confectioners' sugar, 2 tablespoons of milk, and the vanilla extract until a thick, pourable glaze comes together. If the glaze seems too thick, add more milk, one teaspoon at a time, until it reaches the desired consistency. If the glaze is too thin, gradually add more confectioners' sugar.
Drizzle the glaze over the cooled cake.
Let the icing set, and then slice and serve.