Step 1: Prepare the Caramelized Onions
In a large skillet, heat the butter and olive oil over medium heat.
Add the thinly sliced onions and cook, stirring occasionally, until they start to soften, about 5 minutes.
Add the sugar, salt, and pepper. Continue to cook, stirring occasionally, until the onions are golden brown and caramelized, about 20-25 minutes.
Add the beef broth and balsamic vinegar (if using), stirring to deglaze the pan. Cook for another 5 minutes, allowing the liquid to reduce slightly.
Remove the onions from the heat and set aside.
Step 2: Prepare the Ribeye Steaks
Preheat your grill or skillet to medium-high heat.
Rub the ribeye steaks with olive oil and season generously with salt and pepper.
Place the steaks on the grill or in the skillet and cook for about 4-5 minutes per side for medium-rare, or until they reach your desired level of doneness.
If using, add fresh thyme sprigs to the skillet for added flavor while the steaks cook.
Remove the steaks from the grill or skillet and let them rest for 5 minutes before serving.
Step 3: Prepare the Mashed Potatoes
While the steaks are cooking, place the cubed potatoes in a large pot and cover with water.
Bring to a boil and cook until the potatoes are tender, about 15 minutes.
Drain the potatoes and return them to the pot.
Add the milk and butter, then mash the potatoes until smooth.
Stir in the grated Parmesan cheese and minced garlic (if using).
Season with salt and pepper to taste.
Step 4: Serve
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