Preheat oven to 350°F degrees. Combine dry ingredients (except brown sugar) in a large bowl. Set aside.
Cream butter using the paddle attachment on your mixer approximately 30 seconds until light and fluffy. Add brown sugar and beat on medium speed until light, fluffy, and well mixed. Beat in eggs one at a time, scraping down the bowl between additions. Add vanilla and beat again until well-combined.
Stir the dry mixture into the butter, working in batches to give the dry ingredients time to absorb and incorporate. Scrape down the bowl as needed.
Grease a half sheet pan and line with parchment paper (optional).
Use your hands to firmly press approximately ⅔ of the oatmeal mixture into a very thin even layer at the bottom of the pan, making sure to get into all four corners. Use a small offset spatula to prevent a lip from forming at the edges of the pan. Set aside.
In a small, heavy-bottomed saucepan over medium-low heat, stir together sweetened condensed milk, chocolate chips, salt, and butter. Continue stirring until no lumps left and remain and the chocolate is shiny and smooth. Adjust burner as needed, stirring frequently to prevent chocolate from burning.
Turn off the heat, stir in walnuts and vanilla.
Pour chocolate mixture across the surface of the oatmeal layer in the pan, using a spatula to gently push it into all the corners right to the edge of the sheet pan.
Use your hands to tear, crumble, and pinch the remaining oatmeal dough, dropping it in chunks across the chocolate fudge. Try to get some variety in size between chunks.
Bake in 350°F oven for 25-30 minutes until lightly golden brown on top. The chocolate fudge will likely still look a little molten.
Let the tray cool almost completely on a wire rack before cutting into diamonds. To get the diamond shape: cut 5-7 straight lines lengthwise down the sheet tray, then cut across those lines in a diagonal, starting with a corner-to-corner cut to make it easier to replicate the correct angle as you make the rest of your cuts. The diagonal cuts should be about 2″ apart.
The bars can be a bit tricky and stubborn to remove from the pan. I recommend starting with the odd-shaped edge pieces and then working your way toward the center.