Melt your butter and oil in a large skillet. Add in the onions and cook them down on LOW HEAT for about an hour, until they brown and caramelize, stirring occasionally. You can rush this process.
Roasted Garlic Butter:
Preheat your toaster oven to 400℉. After you've trimmed the top of the garlic head to expose the bulbs, drizzle with olive oil and season with salt and pepper. Wrap the garlic head in aluminum foil and bake for 45 minutes or until the garlic is softened and squeezable. Squeeze out the garlic head into a bowl with the softened butter and mix to incorporate.
Herb Mayo:
Mix all of the ingredients for the Herb Mayo in a small bowl. Taste and adjust if needed.
Steaks:
Pat your steaks down with paper towels. Season both sides of each steak generously with salt and pepper.
Heat your pan on high and add in the oil. Lower to medium high and add in the steaks. Sear them on each side for 4 minutes per side. You also need to sear the sides of the steaks - about 1 minute per edge.
Lower the heat to medium and quickly add in the butter, garlic and rosemary. Once melted, carefully tilt your pan to one side and spoon the butter over the steaks continuously.
Medium Rare: 135℉Medium: 145℉Well Done: 160℉
Transfer your steaks to a cutting board and let them rest for 10 minutes prior to slicing.
Assembly:
Slice your Italian bread in half and slice to open them. I scooped out some of the inside of the bread (on the top part only) to give way to the sandwich ingredients.
Spread the bottom piece with the garlic butter, next comes the baby arugula, then the steak slices, then the cheese slices, caramelized onions and lastly the herb mayo! Top with the bread and enjoy.