For the brisket: Put the brisket and broth in a medium high-sided skillet and heat gently over medium heat just until warmed through, about 10 minutes.
For the Texas toast: Heat a cast-iron griddle pan over medium-high heat. Add 4 tablespoons of the butter and melt. Put the bread on the griddle and toast until golden brown, 2 to 3 minutes. Flip and cook the second side until golden brown, another 2 to 3 minutes, adding more butter if necessary.
For the cheesy eggs: Melt the butter in a large nonstick pan over medium heat until the foaming stops. Add the eggs and green onions and cook slowly, stirring, until soft mounds form, 3 to 4 minutes. Fold in the havarti and season with salt and pepper. Transfer to a plate to stop the cooking.
Put the toast on a cutting board. Top each piece with several slices of brisket, some of the eggs and some chow-chow. Serve immediately.