Prepare the cheesecake filling. In a medium bowl, beat the softened cream cheese, sugar, egg, lemon juice, and salt for 2–3 minutes, or until completely smooth and creamy. Set aside.
Make the custard. In a large bowl, whisk the eggs, whole milk, half-and-half, 1/3 cup maple syrup, vanilla, cinnamon, and nutmeg until thoroughly combined.
Prepare the bread. Cut the brioche or challah into cubes. Spread some of the cheesecake filling between pieces of bread and add some of the strawberries to create small sandwiches. Cut the sandwiches into smaller cubes.
Assemble the casserole. Grease a 9×13-inch baking dish. Arrange half of the prepared bread cubes in the dish. Add some of the remaining cream cheese mixture and scatter 1 cup of strawberries over the top.
Add the remaining bread cubes and cream cheese mixture. Slowly pour the custard evenly over everything. Gently press the bread into the liquid so it can absorb the custard.
Cover and refrigerate for at least 2 hours or overnight. This resting period helps the Strawberry Cheesecake French Toast Bake develop its soft, creamy interior.
Preheat the oven to 350°F (175°C). Remove the casserole from the refrigerator and allow it to stand at room temperature for about 10 minutes.
Cover tightly with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for 25–35 minutes, until the top is golden and the center is set. A slight jiggle in the center is fine because the custard will continue setting as it rests.
Prepare the strawberry syrup. Combine the strawberry jam and 1/2 cup maple syrup in a microwave-safe bowl. Heat in 30-second intervals, stirring after each, until smooth and pourable.
Allow the casserole to rest for 5–10 minutes before slicing. Serve warm with the strawberry-maple syrup drizzled over each portion.