In a small saucepan, combine the water through the head of garlic over medium heat. Warm slowly and stir until sugar and salt are dissolved. Turn off the heat and stir in 2 cups of ice cubes to cool it down.
Place the pork steaks in a non-reactive container (a shallow glass or stainless steel dish works well). Pour the cooled brine over the steaks. If necessary, add just enough cool water so the steaks are completely submerged. Cover and refrigerate overnight or at least 12 hours.
Remove the steaks from the fridge 1 hour before you begin roasting. Drain the brine from the steaks and pat them dry with paper towels. Reserve the rosemary and garlic if you'd like. Place the steaks into an oven-safe dish or roasting pan (you can use the same dish you brined in), and place the rosemary and garlic on top. Preheat the oven to 325°F.
Meanwhile, prepare the vinaigrette by whisking all the ingredients together in a small bowl.
Cover the pan with foil, and roast the steaks for 45 minutes. The steaks should reach 140°F in the thickest part when done.*
Preheat your outdoor grill. Clean and oil the grates. Grill the steaks on high for 2 to 3 minutes on each side to sear the meat and get some crispy edges.**
Rest the steaks for several minutes before slicing. Serve with a drizzle of prosecco vinaigrette.