Preheat oven to 350°. Butter a large casserole dish or 9x13-inch pan.
In a large bowl whisk together eggs, evaporated milk or cream, milk, sugar, salt, and vanilla. Whisk together until completely combined.
Add brioche to the egg mixture. Mix together with a flexible spatula.
Add jam. Mix gently until jam is swirled throughout the batter but not completely mixed in.
Transfer mixture to the buttered casserole dish and spread until a fairly even layer.
Scatter strawberries over the top of the batter and gently press them in.
Bake for about 60 minutes or until set in the middle (poke with a pairing knife to check). Remove from oven and allow to cool for 10 minutes before serving.