Trim off the bread crusts and carefully cut the thick slices in half, leaving one side intact. Spread 1½ tablespoons of peanut butter inside each piece of milk bread.
In a shallow bowl, whisk to combine the milk, eggs, cinnamon, and salt. Soak the peanut butter–stuffed bread in the milk mixture for 2 minutes on each side.
While the bread is soaking, melt the butter in a large skillet over medium heat. Add the soaked bread to the pan, cover with a tight lid, and cook until golden brown on the underside, 2 to 3 minutes. Flip the bread and cook the other side, uncovered, until golden brown, 2 to 3 minutes.
Serve the French toast with a drizzle of condensed milk and a slab of butter.
