Heat oven to 475F degrees, place oven rack at middle position. Have baking sheet or broiler pan ready.
Heat a large non-stick skillet or deep pan to medium-high. Add 1 tablespoon oil and heat till shimmering.
In a small bowl, combine 3 tablespoons oil with the fresh thyme and minced garlic. Using your hands, rub this mixture over both pork tenderloins. Add tenderloins to the skillet on your stove and sear on all sides, about 2-3 minutes per side.
Remove meat from the skillet but do not clean out pan, you'll be using it again (If your pan continues to get stuck-on grease and bits in the pan, all the better! We'll be dealing with it and savoring it for the gravy. Don't worry about it now). Place tenderloins on the baking sheet and bake in the hot oven for 10 minutes*. Check for internal temperature and once center has reached 145F degrees, remove from oven (stand to side as you open oven door because oven will be initially smoky), cover with foil and set aside.
In the same pan you seared the meat, add 1 tablespoon butter and heat to medium-high heat. Add the shallots and cook until they barely start to brown. Add the pears to the pan with the shallots and cook, stirring occasionally until shallots are nice and brown and the pears have some of the pan drippings clinging to them. Remove to a plate. Still don't clean out the pan, you're not done with it yet.
In a small bowl, place the 2 tablespoons room temperature butter and 1 tablespoon flour. With a fork, cut the flour and butter together. Note: For gluten-free, replace flour with cornstarch. Set aside.
Here's where you're going to love all or any of the baked on bits in that skillet- Heat the skillet back to medium-high and add the butter mixture, chicken broth, 3 cloves diced garlic and pear nectar. Whisk or stir until butter mixture has incorporated and the bits that were in the skillet have released. Let the mixture boil, stirring occasionally, until it reduces and thickens to desired consistency, about 10 minutes. Taste and add salt and pepper, if desired.
If you want to serve this meal right now, cut the pork into thick slices, place on a platter with pears and shallots on the side. Place extra sprigs of thyme over everything. Pass around the gravy to be poured over.
If you want this dish to become even more tender and flavorful and have the time, do this: Place the pears and shallots over the pork tenderloins still in the baking sheet. Pour half of the gravy over everything, and place remaining gravy in the fridge until ready to serve. Cover the pork with foil. Heat the oven to 250F degrees and place the foil covered pan back in the oven for at least one hour and even up to two (I promise it won't dry out). To serve, plate the pears, shallots and gravy that was poured into the pan. It should have mixed nicely with any pan drippings from the pork. Cut the pork into thick slices and add to plate. Heat the remaining gravy in a small pan or the microwave. Pass this amazingly tender and tasty dish around with the remaining gravy.
Leftovers (if you have any) are amazing and can be refrigerated for up to 2 days.
*Note: If you're going to use the slow roasting method and will be finishing your roast in the 250F oven, you can skip the initial cooking on the high heat. Just make sure you cook the roast for the full two hours at 250F if you skip the initial roasting.