Make the Strawberry Swirl: Combine the strawberries, sugar, water and cornstarch in a small saucepan and cook over low heat, stirring constantly, until the mixture becomes very thick. Set aside and allow to cool to room temperature before using.
Make the Pound Cake: Preheat oven to 325 degrees F. Grease and flour a standard-size Bundt pan.
Using an electric mixer, beat the cream cheese and butter on medium speed until combined and soft, about 2 minutes. Add the sugar continue to beat on medium speed, scraping the bowl once or twice, until the mixture is very light and fluffy, about 5 minutes. Add the eggs one at a time, beating until each one is completely incorporated before adding the next. Scrape down the sides of the bowl, reduce the speed to low, and gradually add the flour until it has all been combined. Add the vanilla extract and salt and mix on low speed until incorporated, about 1 minute.
Spoon about ⅔ of the cake batter into the prepared Bundt pan. Top evenly with the strawberry filling, leaving a 1-inch border around the edge of the pan. Use a thin paring knife to gently swirl the strawberry filling with the cake batter just a few times – less is more. Spoon the remainder of the cake batter on top of the filling and gently spread to the edges of the pan, covering the filling.
Bake for 1¼ to 1½ hours, or until a thin knife inserted into the center of the cake comes out clean. Allow the cake to cool in the pan for 15 minutes, then turn it out onto a wire cooling rack and allow to cool completely before serving. Leftovers can be wrapped in plastic wrap or placed in an airtight container and stored at room temperature for up to 4 days, or in the refrigerator for up to 1 week.