In a small sauté pan, mix 1 tablespoon of olive oil with the basil, lemon juice, and salt. Place it over medium heat and cook for about 1 minute, just until it begins to sizzle. Remove the pan from the heat and set it aside.
Preheat a stove-top grill and drizzle a bit of olive oil on both slices of bread.
Place the bread on the grill, oiled side down. As soon as it's beginning to brown, flip it over and spoon half of the basil mixture on each slice of bread. Immediately add the brie slices on top of each one, turn the heat to low, and cook just until the brie is melted.
Use a metal spatula to move both prepared slices of bread to a plate. Add the strawberries and grapes on one of the halves and drizzle with the balsamic vinegar.
Place the other half on top and gently press it down.
Voilà!
Notes
If you don't have a grill, simply follow the same instructions, only with a satué pan.