Position a rack in the center of the oven and preheat to 350°F. Using a paring knife, make 16 incisions, about ½-inch deep, all over the roast; insert the garlic halves. Season the meat generously with salt and pepper.
Make the glaze: In a small pot over medium-high heat, melt the butter; when the foam begins to subside, add the shallot and cook, stirring frequently, until translucent and soft, 4–6 minutes. Add the port, bring to a boil, then lower the heat to medium-low and cook, stirring occasionally, until the liquid is reduced by a third, 6–8 minutes. Stir in the preserves and vinegar, season to taste with salt and pepper, and cook until smooth and syrupy, about 3–5 minutes more. Remove from heat.
In a large cast-iron skillet over high heat, heat the oil until it shimmers, then add the roast and sear, using tongs or two large forks to turn the meat occasionally, until browned all over, 10–12 minutes. Position the roast bone-side down in the skillet and transfer to the oven. Cook, basting every 15–20 minutes with the glaze, until an instant-read thermometer inserted into the thickest part of the meat reads 120°F, 1 hour 15 minutes for rare. Carve and serve with the remaining glaze on the side.