In a large mixing bowl, whisk together the flour, baking powder, herbes de Provence, salt, and pepper. In a second bowl, whisk together the eggs, yogurt, and olive oil. Pour the mixture over the dry ingredients and stir, using a spatula, until just combined. Fold in the cheese, ham, and olives. Transfer the batter to the prepared loaf pan. Use the spatula to smooth out the surface.
Bake until the bread is puffed and golden and a toothpick inserted in the center comes out clean, about 45 minutes. Remove from oven and let cool for 15 minutes. Pull on the parchment paper to unmold the cake, running a knife around the pan if necessary. Transfer to a wire rack and let cool completely.
Slice the bread and serve at room temperature, or warm in a 300°F (150°C) oven for 10 minutes before serving.
STORAGE: The flavors of this French savory cake keep developing as it sits, which makes it even better the next day. If you can, make it in advance, let it rool completely, then wrap it tightly in plastic wrap. Warm in a 300°F (150°C) oven for 10 minutes before serving.
French savory cake will keep refrigerated, tightly wrapped, for up to 1 week, or frozen for up to 1 month.
NOTE: The batter can also be baked in two small loaf pans (6 x 3.5 in / 15 x 9 cm) for about 25 minutes, or in a standard muffin pan. Line the pan with parchment paper cups. Divide the batter between the cups and bake for 20 minutes, or until the savory cupcakes are lightly golden and a toothpick inserted in the center comes out clean.
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