Preheat your oven to 175°C (350°F) and butter an 8.10-inch (20.25cm) baking dish.
In a large bowl, whisk together the eggs, sweetened condensed milk, milk, and cinnamon until smooth.
4 Large Eggs, 396 Grams Sweetened condensed milk, 120 Milliliters Whole milk, ½ Teaspoon Ground cinnamon
Dip each slice of brioche (or sliced soft bread) quickly into the egg mixture to coat, then arrange the slices neatly in the prepared baking dish. Do not let the bread soak, brioche absorbs quickly.
1 Brioche loaf
In a small saucepan over medium heat, melt the butter, brown sugar, and vanilla together. Stir constantly until the sauce is smooth and slightly bubbly, about 6-8 minutes. Remove from heat.