Stir together brown sugar and next 3 ingredients. Rub steak with sugar mixture, and let stand 5 minutes.
Heat 1 Tbsp. olive oil in a cast-iron grill pan over high heat. Add steak; cook, turning once, until seared, 12-16 minutes for medium-rare. Remove from skillet; cover loosely with aluminum foil. (Alternatively, cook steak on gas or charcoal grill.)
Meanwhile, cook potatoes in remaining 3 Tbsp. hot oil in a large skillet over medium-high heat, stirring occasionally, 10 to 12 minutes or until golden. Remove from skillet.
Melt 2 Tbsp. butter in skillet. Add onion; cook, stirring often, 5 to 7 minutes or until tender. Add artichokes and garlic; cook, stirring often, 5 minutes. Stir in parsley, next 2 ingredients, potatoes, and remaining 1 Tbsp. butter; cook, stirring often, 2 to 3 minutes.
Cut steak diagonally across the grain into thin slices, and serve with potato mixture. Add salt and pepper to taste.
Note: We tested with Alexia All Natural Oven Reds with Olive Oil, Parmesan & Roasted Garlic potatoes.