Pat tenderloins dry and season with salt and pepper. Heat oil in a skillet and brown pork for about 1 minute on each of 4 sides, then place in one layer in a 5- to 6-quart oval slow cooker.
Add garlic, broth and soy sauce around the pork. Cover and cook on low for about 1 1/2 to 2 1/2 hours, beginning temperature checks after 1 hour and removing each tenderloin as its thickest center reaches 145°F.
Transfer pork to a foil-lined broiler-safe pan and rest for at least 3 minutes. Pour the cooking juices into a saucepan, skim fat and add balsamic vinegar and brown sugar.
Simmer for 5 to 8 minutes until reduced to about 3/4 cup. Stir cornstarch mixed with cold water into the sauce and simmer for 1 minute until it clings to a spoon.
Brush pork with a thin layer of glaze and broil 6 inches from the heat for 1 to 2 minutes until lightly caramelized, watching constantly. Rest for 3 minutes, slice across the grain and spoon a little remaining glaze over the slices.