Preheat oven to 350°F. Grease one 8-inch cake pan, line the bottom with parchment paper, and grease the parchment paper.
In a small bowl, combine flour, baking powder, and chopped figs, stirring until figs are coated in flour mixture. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a hand mixer), cream butter and sugar on medium speed until light and fluffy (2-3 minutes).
Add eggs one at a time, beating just until combined in between. Scrape bowl as needed.
Add vanilla and almond extracts and beat on low speed just until combined.
Add flour mixture, mixing on low speed until combined. Scrape the bottom of the bowl to make sure there are no bits of flour mixture hiding there.
Add milk and mix on low speed until combined.
Pour batter into the prepared pan and smooth the top.
Bake for 30-40 minutes, or until a toothpick inserted into the center comes out clean (or mostly clean with a few moist crumbs on it). Cool in the tin for about 10 minutes, then carefully remove from the pan and set on a cooling rack to cool completely.
Cream Cheese Frosting
Using a stand mixer fitted with the paddle attachment (or a hand mixer), mix butter and cream cheese on medium speed until well-mixed and fluffy, about 2-3 minutes.
Add vanilla bean paste or extract and mix well.
Add powdered sugar a little at a time, mixing well in between.
Once everything is well combined, beat at medium-high speed until frosting is fluffy. If frosting becomes a little too melty, pop it in the refrigerator to firm it up a bit.
Once cake is cool, spread the fig jam in a thin layer over the top of the cake.
Spread all of the frosting on top of the fig jam. Top with whole figs, and serve!
Stored any leftover cake in an airtight container in the refrigerator (but bring up to room temperature before serving for the best flavors and textures).