In a mixing bowl, combine the tomato, corn, garlic, lime juice, and 1 tablespoon of olive oil. Season to taste with salt and pepper, stir in the basil, and taste again for acidity and salt. Set aside.
Heat a large grill pan over high heat until smoking. Toss the sliced beef with 1 tablespoon of olive oil and season generously with salt and pepper. Add the beef to the pan and cook untouched until almost cooked through and charred in places. Toss the meat with tongs to redistribute and cook until completely cooked through, about 30 seconds longer.
Remove the beef to a plate to rest, drizzle remaining tablespoon of oil over it, and grill the baguette pieces for a minute to soften and warm them.
Spread mayonnaise on one side of each baguette and top with the steak. Spoon relish over the other half, top with avocado, repeat with remaining sandwiches, and serve.