Adjust oven rack to middle position and preheat oven to 200ºF (93ºC). Set a wire rack in a rimmed baking sheet. Arrange bread in a single layer on the rack and cook in oven, turning once, until dried but not toasted, about 10 minutes. Transfer to a plate and line a separate plate with a double layer of paper towels. Set baking sheet aside.

In a large mixing bowl, whisk together eggs, sugar, and salt until thoroughly combined. Add milk and whisk to blend.

In a large Dutch oven or wok, add oil until it measures 2 inches deep and heat over high heat to 350ºF (177ºC). Meanwhile, lay 4 slices of bread out on a work surface and spread each slice with 2 tablespoons peanut butter , then top each with a slice of bread.

Whisk egg mixture to recombine, then, working with 1 sandwich at a time, soak sandwich in egg mixture, flipping as needed, until saturated, about 2 minutes. Allow any excess egg mixture to drip into the bowl, then carefully add soaked sandwich to hot oil and fry until golden brown on bottom side, about 2 minutes. Using tongs and/or spider skimmer, gently flip the sandwich and continue to fry until golden brown on the other side, about 2 minutes. Transfer the French toast to the prepared plate, then place on wire rack and keep warm in the oven. Return oil to 350ºF (177ºC) and repeat with remaining sandwiches.

Divide the French toast among four plates, top with pats of butter and a generous drizzle of condensed milk. Serve.