Heat a skillet or an electric griddle to 325-350 degrees F.
Using a paring knife, cut halfway into each slice, in the center, creating a ‘pocket’ that your fruit and cream cheese will get stuffed into. Spread 1 oz of cream cheese into each 'pocket' and divide and stuff sliced strawberries inside each pocket.
In a large mixing bowl, combine the eggs, half and half, milk, sour cream, sugar, and vanilla extract. Whisk until sugar dissolves. Use a hand blender or an immersion blender to get the job done quicker.
Soak two of the bread slices in the mixture for about 30 seconds on each side. Meanwhile, over medium heat, melt 1 Tablespoon of butter + 1 teaspoon oil in a skillet pan. Place 2 slices into the pan and cook until gold brown on each side, about 3-4 minutes on each side. Melt more butter + oil in skillet pan for the next batch. Serve immediately with more fresh berries, whipped cream, and powdered sugar.