Dry-Brine the Rump Roast (Optional, But Recommended)
Pat rump roast dry with paper towels.
Season all over with kosher salt.
Place on a wire rack, uncovered, in the fridge for 3 days.
After 3 days, pat dry again. The pepper goes on after the sear, not before it, because it burns before the crust forms.
Sear & Coat with Garlic Olive Oil
Preheat oven to 225°F (107°C).
Heat 1 tablespoon olive oil in a cast-iron pan over medium-high heat.
Sear roast on all sides until deeply browned, about 3 minutes per side. You'll know it's ready to flip once it releases from the pan. It sticks because the crust is still forming, so don't nudge it around if it's not releasing. The protein will almost always tell you when it's ready.
In a bowl, mix grated garlic with 2 tablespoon olive oil.
Brush garlic oil mixture all over seared beef.
Slow-Roast for Perfect Medium-Rare
Transfer to roasting rack and roast until internal temp hits 120°F (rare) or 125°F (medium-rare), about 2–2.5 hours.
Remove from oven, tent loosely with foil, and rest for 20 minutes.
Make the Balsamic Caramel Reduction
In a saucepan, add aged balsamic, honey, and thyme.
Simmer over medium heat, stirring occasionally, until thickened to syrup (8–10 minutes).
Remove thyme. Whisk in butter until glossy.
To Plate
Slice beef thinly against the grain.
Drizzle with warm balsamic caramel reduction.
Top with shaved Parmigiano Reggiano.
Finish with aged balsamic drizzle and Maldon salt.