Preheat oven to 375°F (190°C).
For cake: In a 13×9-inch baking dish, stir together strawberries, 1⁄4 cup (50 grams) sugar, and 1⁄4 teaspoon salt until well combined.
Bake until berries are fragrant, soft, and have released ample juices, 30 to 40 minutes, stirring every 10 minutes. Reduce oven temperature to 325°F (170°C).
Strain berries through a fine-mesh sieve over a medium bowl, reserving liquids and solids. Let berries cool completely, 15 to 20 minutes; chop into 1⁄4-inch pieces, and return to sieve over bowl to collect any extra juices.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and remaining 3¼ cups (650 grams) sugar at medium-high speed until light and fluffy, 5 to 7 minutes, stopping to scrape bottom and sides of bowl and paddle. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In another large bowl, whisk together flour, baking powder, and remaining 2¼ teaspoons (6.75 grams) salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with buttermilk, beginning and ending with flour mixture, beating just until combined after each addition and stopping to scrape bottom and sides of bowl. Using a spatula, fold in chopped strawberries until well combined.
Spray an 18-cup tube pan with baking spray with flour; using a pastry brush, spread any excess spray evenly in pan, blotting brush with a paper towel as needed. Spoon batter into prepared pan, smoothing with an offset spatula. Forcefully tap pan on a kitchen towel- lined counter several times to settle batter and release as many air bubbles as possible.
Bake until a wooden pick inserted near center comes out clean and an instant-read thermometer inserted near center registers 205°F (96°C), 1 hour and 25 minutes to 1 hour and 35 minutes, rotating pan after 40 minutes of baking and loosely covering with foil to prevent excess browning, if necessary. Let cool in pan on a wire rack for 15 minutes. Remove from pan, and let cool completely, top side up, on a wire rack.
For glaze: In a small bowl, whisk together 3 to 4 tablespoons (45 to 60 grams) reserved roasted strawberry juice, confectioners’ sugar, melted butter, and salt until smooth and well combined; spoon onto cooled cake. Store in an airtight container for up to 3 days.
