Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter and set aside.
Spread bread cubes on a baking sheet and toast in the oven for 8-10 minutes until lightly golden and dried out. Transfer to the prepared baking dish.
In a large bowl, whisk together eggs, milk, heavy cream, granulated sugar, vanilla extract, and salt until smooth and sugar is dissolved.
Toss strawberry quarters with cornstarch in a small bowl until evenly coated.
Pour the custard mixture over the toasted bread cubes, pressing down gently with a spatula to ensure all pieces are soaked. Let rest for 20-30 minutes at room temperature.
Fold the strawberries into the soaked bread mixture, distributing them evenly throughout. Drizzle melted butter over the top and sprinkle with turbinado sugar.
Bake for 45-50 minutes until the top is golden brown and the center jiggles only slightly when gently shaken. A knife inserted in the center should come out mostly clean.
Remove from oven and let cool for 10 minutes before serving. The pudding will continue to set as it cools.
