Preheat oven to 350.
Brush the tops of each baguette slice with the olive oil (1 TBSP). Place on a baking sheet, and bake until lightly browned, about 8 minutes.
Meanwhile, quarter the cherry tomatoes and chop the artichoke hearts and basil. Combine into a bowl. Add sea salt and remaining 1 TSP EVOO, and toss to evenly mix together.
When bread is done, remove from oven and place crostini on a plate. Use a butter knife to spread some goat cheese onto each slice, then top each with a large spoonful of the veggie mixture. Serve them while they're warm!