To make the brine: Combine all the brine ingredients in a large pot, cover, and bring to a boil. Boil for 1 minute, stirring to dissolve the salt. Remove from the heat and cool completely, then chill before using. The brine can be refrigerated for up to three days.
Pour the brine into a container large enough to hold the pork and add the pork. Refrigerate for 4 hours (no longer, or the pork may become too salty).
Remove the pork (discard the brine) and rinse under cold water. Pat dry with paper towels, or let air-dry. Let the tenderloin sit at room temperature for 30 minutes.
Preheat the oven to 350°F. Set a roasting rack in a roasting pan.
Pour some canola oil into a large frying pan or small roasting pan large enough to hold the pork and heat over medium-high heat until hot.
Season the tenderloins with kosher salt and pepper, add to the pan and sear, turning them occasionally, until golden brown on all sides, about 6 minutes.
Add the butter, garlic, and thyme and cook, tilting the pan and using the spoon to baste the pork with the juices, for 2 minutes.
Transfer the meat to the roasting rack. Top with the garlic, rosemary, and thyme. Roast until the internal temperature is 135° to 140°F (use the latter if you prefer your pork less pink), about 20 minutes. Remove from the oven and let the meat rest for 15 minutes for medium-rare to medium.
Slice the pork on the diagonal into ½-to-¾–inch-thick slices. Arrange the slices on a serving platter and garnish with the garlic and thyme.