In a mixing bowl, combine the softened cream cheese, sour cream, lemon juice, powdered sugar, and vanilla extract. Using a whisk, blend until the mixture is smooth and creamy. Gently fold in the thinly sliced strawberries, being careful not to mash them. Set the filling aside.
Take your stale brioche slices and make a pocket in each slice. This can be done by carefully cutting each slice horizontally, ensuring not to cut all the way through. Fill each pocket with the strawberry cream cheese mixture, spreading it evenly inside, and set aside.
In another mixing bowl, whisk together the eggs, half and half, cinnamon, and additional vanilla extract until well combined and frothy.
Dip each stuffed slice of bread into the custard mixture, allowing it to soak for a few moments on each side. Be careful not to let it become too soggy, as you want the bread to hold its shape while cooking.
In a large frying pan or griddle, heat 1 tablespoon of vegetable oil and 2 tablespoons of butter over medium heat. Once hot, place the soaked stuffed French toast slices in the pan, cooking in batches if necessary. Fry for about 3-4 minutes on each side or until golden brown.
Once cooked, remove the French toast from the pan and keep warm in a low oven if cooking in batches. Serve immediately, dusted with powdered sugar, and topped with fresh berries, syrup, or whipped cream as desired.