01 - Combine warm milk, sugar, and yeast in a bowl. Let stand for 5 minutes until the mixture becomes foamy and activated.
02 - In a large bowl, mix flour, salt, softened butter, Parmesan cheese, and minced garlic. Pour in the activated yeast mixture and knead until a smooth, elastic dough forms, about 8 minutes by hand or 5 minutes with a stand mixer.
03 - Cover the dough with a clean towel and let it rise in a warm spot until doubled in size, approximately 1 hour.
04 - Divide the dough into 8 equal portions and shape into balls. Place on a parchment-lined baking sheet. Brush each roll with beaten egg wash and sprinkle with extra Parmesan if desired. Bake at 375°F for 18–20 minutes until golden brown. Cool slightly before handling.
05 - Season the filet mignon medallions generously with salt and black pepper on both sides. Heat olive oil in a skillet over medium-high heat. Sear the medallions for 2–3 minutes per side for medium-rare, or adjust to your preferred doneness. Add butter during the last minute of cooking and baste the medallions. Transfer to a plate and rest for 5 minutes.
06 - In a small bowl, combine softened butter, minced garlic, chopped parsley, and a pinch of salt. Mix until well incorporated.
07 - Slice each roll in half horizontally. Spread the garlic butter mixture generously on both the bottom and top halves. Layer arugula leaves, a filet mignon medallion, a slice of provolone or Swiss cheese, and caramelized onions on the bottom half. Cap with the top half of the roll. Serve immediately while warm.