In a large mixing bowl, whisk together flour, sugar, salt and yeast. Add warm water and olive oil, and using a rubber spatula or wooden spoon, stir until no more dry spots remain. Cover the bowl and let it sit for 15 minutes.
Uncover the bowl. Using the stretch-and-fold method, pull the edge of the dough from one side of the bowl and press into the center. Repeat along the edge of the dough, about 8 times, until you’ve made it all the way around the dough ball. (Using a wet hand will make this easier.) Cover the dough and let rest another 15 minutes.
Repeat this process for a total of four times. After the fourth time, cover the dough once more and let it sit in a warm place (72-78°F) to rise until doubled in size, about 1 hour.
Meanwhile, make the almond filling. Toast the almond flour in a small skillet over medium heat until lightly golden brown, about 15 minutes. Let cool slightly. Combine softened butter and brown sugar in a mixing bowl and beat it with a wooden spoon for about a minute until pale and fluffy. Add eggs and almond extract and whisk until fully combined. (The mixture may look separated at this point—it will come together when you add the dry ingredients.) Add the toasted almond flour, all-purpose flour and salt and whisk until smooth. Set aside until your focaccia has risen.
When the focaccia is ready, crumble about two-thirds of the almond filling all over the top of the fluffy dough. Using the stretch-and-fold method one last time, gently pull the edges of the dough to the other side to cover the almond filling. (Be sure you’re doing this carefully, so you don’t deflate your dough.)
Cover the bottom and sides of your braiser with olive oil. Using a wooden spoon or rubber spatula, carefully roll the dough onto the braiser. Using your hands, gently pad the surface of the dough to spread it out, then drizzle it with more olive oil. Cover and place again in a warm place (72-78°F), and let it rise for 1.5 hours. (The dough should be pressing against the top of the glass at this point.)
Preheat oven to 425°F.
Uncover the focaccia, and using a spoon, dollop the remaining almond filling all over the top of the dough, then drizzle with more olive oil.
Using your fingers, place dimples in the dough all over, all the way down to the bottom of the braiser. Sprinkle with sliced almonds and bake for 16-18 minutes until the focaccia is fully baked and golden brown on top. (If some parts are browning too quickly, tent with foil.) Remove from the oven.
For the optional glaze, mix powdered sugar, almond extract, and heavy cream until smooth, adding more cream, as needed. Drizzle all over the top of the focaccia and serve.
