Steak with Parmesan Butter and Balsamic Glaze

INGREDIENTS

• 2 tablespoons grated Parmesan cheese plus Parmesan cheese shavings
• 1 1/2 tablespoons butter, room temperature
• 1 12-ounce rib-eye steak
• 1 teaspoon olive oil
• 1/4 cup balsamic vinegar
• 1/4 cup finely chopped shallots
• 1/2 teaspoon (packed) dark brown sugar
• 4 cups (lightly packed) arugula or mixed greens
• 2 large lemon wedges