Add the goat cheese with 2 tablespoons of olive oil to the bowl of a mini food processor. Season with a pinch of sea salt and add the chives and thyme but reserving some for garnish. Process together until whipped, a couple of minutes.
Transfer the whipped goat cheese to the refrigerator until ready to use.
Heat up a cast iron grill pan or griddle on medium high flame.
Slice the baguette into 3/4 inch slices. Add them to the hot grill pan and cook for about 1 minute on each side until nice charred grill marks form.
Use the garlic clove and rub one side of each of the grilled slices of bread to your liking. Gently brush with some olive oil and sprinkle with sea salt.
Scoop some of the whipped goat cheese on top of each of the crostini and garnish with the reserved herbs. Serve promptly.