Move the oven rack to the third position below the broiler. Set the broiler to high.
Slice the baguette into 1/2-inch thick slices. Arrange the slices in a single layer on a sheet pan. Depending on the size of your baguette, you may need two pans.
Brush both sides of the bread slices with the olive oil. You may need an extra tablespoon of oil if your baguette is on the large side.
Broil the baguette slices for 1-2 minutes with the door closed until golden brown around the edges.
Flip each toast and broil the second side for 30-90 seconds until the bread is golden and toasted. Watch closely to prevent burning. Remove the pan from the oven and turn off the broiler.
Cut a clove of garlic in half lenghtwise and rub the cut end of the clove all over the warm toasts. Flip the toasts over and rub the underside with garlic as well.
Return the crostini to the oven that is off, but still warm and heat for 1 minute. This will tone down the spiciness of the garlic. After heating, sprinkle with sea salt and serve.