Combine the oil, shallots, garlic, salt, and pepper in a medium bowl; add the steak, and toss to coat.
Tear or cut 4 (18-inch) squares of heavy-duty aluminum foil. Cut the steak into 4 equal pieces. Place one steak piece in the center of each foil square. Drizzle with any remaining olive oil mixture. Bring the sides up and over the steak; double-fold the top and sides of the foil to tightly seal. Refrigerate 12 to 24 hours.
Heat a camping stove or grill to very high (about 450° to 500°F), or fit to grilling grate directly over the heat source, or place directly on hot coals. Cook until desired degree of doneness, about 4 to 5 minutes per side.
Combine the vinegar, brown sugar, and thyme in a small saucepan on the camping stove or grilling grate. Bring to a boil, and cook, stirring occasionally, until the mixture is reduced to about ½ cup and thickened, about 20 minutes. Serve the sauce with the steaks.