Step 1

Preheat oven to 350°F. Beat butter and 3 cups of the granulated sugar with a heavy-duty electric stand mixer on medium speed until light and fluffy, about 2 minutes. Add eggs, 1 at a time; beat on low speed just until incorporated after each addition. Stir in vanilla and almond extract.

Step 2

Whisk together flour and 1/2 teaspoon of the salt in a medium bowl. Add to butter mixture alternately with half-and-half, beginning and ending with flour mixture; beat on low speed just until combined after each addition. Pour batter into a greased and floured Bundt pan. Bake in preheated oven until a wooden pick inserted in center comes out clean, about 1 hour and 15 minutes.

Step 3

During last 20 minutes of baking time, process strawberries and remaining 1/2 cup sugar and 1/4 teaspoon salt in a food processor until smooth, about 45 seconds. Pour mixture through a fine wire-mesh strainer into a bowl; discard solids. Set aside 1/2 cup strawberry mixture.

Step 4

Whisk together water and cornstarch in a small bowl. Combine cornstarch mixture and remaining strawberry mixture in a small saucepan. Cook over medium-high, whisking constantly, until mixture comes to a simmer. Reduce heat to medium, and cook, whisking constantly, just until mixture begins to thicken, about 1 minute. Remove from heat.

Step 5

Cool cake in pan on a wire rack 5 minutes. Using a long wooden skewer, poke holes about 1/2 inch apart into bottom of cake, wiggling skewer slightly to make holes about 1/8 inch wide. (Do not poke skewer all the way through top of cake.) Pour warm strawberry syrup over cake. Let stand until syrup is absorbed and pan is still warm but cool enough to handle, about 20 minutes. Invert cake onto rack, and cool completely, about 1 hour.

Step 6

Whisk together powdered sugar and reserved 1/2 cup strawberry mixture in a medium bowl until smooth. Pour evenly over cooled cake.