I do these a couple times a year 1) Christmas tradition 2) my wife and I for valentines day and I face the same problem. Before I start disclaimer; USDA recommends a minimum internal temp of beef to be 145 degrees. So, What are you cooking it on? When I do my prime rib on a
Weber kettle set up for indirect or on my horizontal offset I put the thermometer probe in on the side closest to the heat source and pull it at IT 130 (maybe 135 at most depending on where my attention is!). Let rest without being covered and on the counter to carve within 30 min. The thinner side closer to the heat will be a few degrees more done to make your wife happy and further away from heat source will be a little less done to make you happy.
If you are using a MES/electric/propane smoker etc you should have one side that runs hotter than the other, follow the same concept. At a minimum remember to keep the thickness of the meat in mind. If the thickest part is IT 130-135 it's in your zone and the thinner parts of the cut will be in your wifes.
Now Sir, can I recomend the recipe? It's the same one I got from Webers cook book a decade ago and is what my wife and family are always excited about. Use Herbs de province as a rub, that's the easy part, the rest is labor intensive. But for 10 years each Christmas my family gets involved with the process, wine in hand, and its a blast. Also, for the past 9 valentines my wife and I make the sauce together and its fun and romantic . . . with wine and good music. In both events the sauce is absolutely amazing and makes the meat perfect for festive or romantic occasions. I'm trying to say, don't be afraid of the work, it is worth it.
What I do From Weber:
INGREDIENTS
SAUCE
Extra-virgin olive oil
1 medium carrot, roughly chopped
2 ribs celery, roughly chopped
1 medium yellow onion, roughly chopped
5 medium garlic cloves, crushed
2 tablespoons tomato paste
3 cups beef broth
1 cup dry red wine
¼ cup balsamic vinegar
2 bay leaves
1 tablespoon finely chopped fresh rosemary leaves
Freshly ground black pepper
4 tablespoons unsalted butter
Kosher salt
1 boneless rib roast, about 5 pounds, trimmed of excess fat
2 tablespoons herbes de Provence
INSTRUCTIONS
In a large saucepan over high heat, warm 2 tablespoons oil. Add the carrot, celery, and onion and cook until the vegetables begin to brown, 6 to 8 minutes, stirring occasionally. Add the garlic and cook for about 2 minutes, stirring occasionally. Reduce the heat to medium, add the tomato paste and cook for about 2 minutes, stirring occasionally. Add the broth, wine, vinegar, bay leaves, rosemary, and ½ teaspoon of pepper. Mix well. Bring to a boil over high heat and then reduce the heat and let simmer for 45 minutes.
Strain the sauce through a sieve into a medium saucepan, pressing down on the solids with the back of a spoon. Continue to simmer until about ¾ cup of liquid remains, about 45 minutes. Add the butter 1 tablespoon at a time, whisking to help melt each piece into the sauce. Season with salt and pepper. Remove the sauce from the heat.
Allow the beef to stand at room temperature for 30 to 45 minutes before grilling. Lightly brush or spray the roast all over with oil and season with the herbes de Provence and salt and pepper.
Cook your prime rib as discussed above and serve with the sauce, warm the sauce if needed!
Good luck! Have fun!