Preheat the oven to 350°F (175°C). Grease a bundt cake pan with oil spray, spread it evenly using a paper towel or napkin, remove any excess, and dust lightly with all-purpose flour. Tap gently to coat all corners, then discard the excess flour. Set aside
In a medium bowl combine the flour, salt, and baking powder. Whisk for a few seconds until evenly mixed and set aside
Drain the syrup from the figs, pat them dry, cut them in half, then in quarters, and into medium-sized pieces. Set aside
In a large bowl add room-temperature unsalted butter (if using salted butter, skip the salt in the dry ingredients) and brown sugar. Beat at medium speed for 1–2 minutes, then increase to high speed and mix for 5–7 minutes until light, fluffy, and creamy. Stop the mixer occasionally to scrape the bottom and sides of the bowl.
Add one egg at a time, mixing for about 40 seconds or until fully combined before adding the next. Repeat until all eggs are incorporated
Stop the mixer before adding dry ingredients to avoid a mess. Add one-third of the dry mixture, mix on low speed just until combined, then add half of the milk. Repeat with another third of the dry ingredients, the remaining milk, and the final third of the dry ingredients. Mix only until everything is combined, do not overmix.
Gently fold the chopped figs or fig preserves into the batter with a spatula until evenly distributed. The batter will look creamy and slightly darker if using black figs.
Pour the batter gently into the prepared bundt pan, spreading it evenly with a spatula. Bake on the middle rack for 55 minutes, or until a bamboo stick inserted in the center comes out clean.
Let the cake rest for about 10 minutes before flipping it onto a serving plate.