Pat 2 pork tenderloins dry with paper towels. Season all over with 1 tsp black pepper and 2 tsp salt. Let sit at room temperature until ready to cook.
Meanwhile, cut 2 medium red onions through the core. Trim off ends, peel, and slice into ½"-thick wedges lengthwise. Transfer to a medium bowl and set aside.
Heat 2 Tbls extra-virgin olive oil in a large skillet over medium-high until shimmering. Sear tenderloins until golden brown on each side, about 2 minutes per side, 6–8 minutes total. Using tongs, transfer pork to a plate.
Cook onion, 1 Tbls extra-virgin oil, and 1 tsp salt in same pan in a single layer over medium-high heat, tossing occasionally, until well browned and beginning to soften, about 5-10 minutes.
Meanwhile, whisk 5 Tbls honey, 1 tsp red pepper flakes, 1 cup red wine vinegar, and ¼ cup water in a glass measuring cup and add to pan once the onions are browned and softened. (Make sure you get all that honey!) Bring to a simmer.
Return pork to pan and cook, turning every 5 minutes and reducing heat as needed to keep sauce at a low simmer, until an instant-read thermometer inserted into the thickest part of the meat registers 140°, 15-25 minutes. (Start testing for doneness after 10 minutes; pork will cook differently depending on the size of the tenderloin you're working with. It’s important to use a thermometer in this case because it’s very easy to overcook a lean cut like this, and nobody likes dry pork!) Transfer pork to a cutting board to rest. This will lock in all the juices and let the pork continue to cook just a bit.
Continue to cook sauce, stirring occasionally, until thick and syrupy, 3–5 minutes. Remove from heat and stir in cold butter until fully incorporated.
Slice pork tenderloin on a diagonal. Divide among plates and spoon onion sauce over. Serve