Preheat the oven to 350°F. Grease a (8 ½X4 ½-inch) loaf pan with olive oil and dust with flour (or use baking spray).
In a large mixing bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon.
In a separate medium mixing bowl, whisk together the olive oil, brown sugar, honey, eggs, Greek yogurt, and vanilla extract until fully combined.
Pour the wet ingredients into the dry ingredients and mix gently with the whisk just until combined. Add the chopped figs and gently mix with a rubber spatula until evenly distributed through the batter.
Pour the batter into the prepared pan. Top with the quartered figs and sprinkle on the chopped hazelnuts. Bake for 60 to 70 minutes, or until a toothpick inserted into the center of the loaf comes out clean.
Let the loaf cool in the pan for 15 minutes before turning it out onto a wire rack to cool completely.
Slice and serve. The cake will keep for up to 3 days tightly wrapped at room temperature.
