Chop/mince two of the anchovy fillets. Heat the olive oil over medium heat in a high-rimmed skillet or saucepan. Add the anchovy fillets to the oil with the thyme, grated garlic, and onions. Let the onions cook for about 20 minutes, stirring occasionally, caring not to burn. After 20 minutes, bring the heat to medium-low and add a pinch of salt. Stir, and let the onions simmer for another 15-20 minutes, or until golden in color and incredibly soft. Remove the pan from the heat and let the onions cool.
Preheat the oven according to the directions of your flatbread or pizza shell.
Once the onion mixture has cooled, evenly spread it over the flatbreads as your base. Place the anchovies over the flatbread in a criss-cross pattern, and finally, top it all off with the olives.
Bake the flatbreads as per the directions on the packaging. When done, remove your flatbreads from the oven and garnish with freshly chopped parsley, if desired.