For the crust, crumble yeast and mix with about 200 ml (approximately 3/4 cup) lukewarm water. Mix flour with a generous pinch of salt. Stir 4 tablespoons olive oil into yeast mixture and knead into flour mixture into a smooth, pliable dough. Knead additional flour or water into dough if necessary to keep dough from getting too sticky. Cover dough and let stand in a warm place until approximately doubled in volume, about 1 hour.
For the topping, peel onions and garlic. Cut onions into rings. Mix anchovies, garlic and remaining oil and mash until slightly lumpy. Drain olives well.
Preheat oven to 200°C (approximately 400°F).
On a lightly floured surface, knead dough briefly and roll into a rectangle about 20 x 30 cm (approximately 8 x 12 inches), pinching around the edge to form a slight rim on crust. Place crust on a baking sheet lined with parchment paper. Spread anchovy mixture over crust, leaving a narrow border free. Sprinkle onions, olives and thyme sprigs over crust and bake until golden brown, about 30 minutes. Cut pissaladière in pieces and serve warm or cooled as desired.