Add the brown sugar, salted butter, heavy cream, and salt to a small saucepan.

Place the saucepan over medium heat.

Stir as the butter melts and the sugar starts dissolving.

Let the mixture bubble gently.

Simmer the caramel sauce for 2 to 3 minutes.

Stir often while the sauce simmers.

Remove the pan from the heat.

Stir in the vanilla extract.

Warm the sauce gently if it thickens while the French toast cooks.

Add 1 tablespoon of cream if needed to loosen the sauce.

Whisk the eggs, whole milk, heavy cream, brown sugar, vanilla extract, cinnamon, and salt in a shallow dish.

Keep whisking until no egg streaks remain.

Warm a large skillet over medium heat.

Add a small pat of butter to the skillet.

Let the butter melt and coat the pan.

Dip one bread slice into the custard for 10 to 15 seconds.

Turn the bread once and soak the second side.

Let extra custard drip back into the dish.

Place the bread slice in the warm skillet.

Cook for 2 to 3 minutes per side, until golden.

Transfer the cooked slice to a plate or a warm oven.

Repeat with the remaining bread slices.

Add fresh butter between batches as needed.

Wipe dark butter bits from the skillet if needed.

Keep cooked slices warm in a 200-degree oven on a rack over a baking sheet if needed.

Drizzle warm caramel sauce over the French toast before serving.