Preheat the oven to 400°F. Arrange the hoagie rolls, cut side up on a baking sheet and set aside.
If necessary, trim any excess fat from the strip steaks, then cut them across the grain into thin slices. Place the steak in a bowl, drizzle with about 1 tablespoon of olive oil, add the Worcestershire, season with salt and pepper and toss to coat. Set aside.
Fry the bacon in a large skillet until crisp. Drain on paper towels, crumble into small pieces and transfer to a small bowl.
Drain the bacon fat from the pan, but don’t wipe it out. Heat over medium heat and add the sliced onion. Cook, stirring occasionally, until the onion is soft and lightly caramelized, 8 to 10 minutes.
Transfer the onions to the bowl with the bacon. Stir in the mayonnaise and horseradish and season to taste with salt and pepper. Divide the mixture between the 4 hoagie rolls.
Turn the heat on the pan up to medium-high and add the steak. Cook until lightly browned, 2 to 3 minutes. Divide the steak amongst the rolls and top with a slice of Havarti cheese.
Place the baking sheet in the oven and bake until the cheese is melted and rolls are lightly toasted, 3 to 4 minutes.