Prep: Preheat oven to 375 F/190 C. Line 2 baking sheets with parchment paper.
Brown butter: Melt butter in a small saucepan over medium-high heat, swirl pan occasionally to loosen the milk solids from the bottom of the pan. Remove from heat when the milk solids are golden brown and the butter has a nutty aroma, about 1 to 3 minutes. Bloom ground cinnamon in warm butter.
Make the cookie dough: Whisk flour, salt, and baking soda together in a mixing bowl until no lumps remain. Add brown sugar, granulated sugar, and oil to browned butter and whisk until combined. Stir in sourdough discard, egg, egg yolk, vanilla until the mixture is smooth. Using a wooden spoon or spatula, stir in flour mixture until fully combined, about 1 minute.
Add mix-ins: Stir in oats, and mix-ins and stir until evenly distributed (your mixture will be thick and stiff).
Shape: Use a large cookie scoop (about 3 tablespoons) to portion out your cookie dough. Arrange cookie dough balls 2 inches apart on prepared sheets, 10 dough balls per sheet. Use your fingers to flatten each one slightly before baking. Bake, 1 sheet at a time, and refrigerate the other cookie sheet as the cookies bake.
Bake: Bake until cookie edges are slightly browned and crisp with centers soft but not wet, 10 to 12 minutes. Let the cookies cool on the baking sheet for 5 minutes before moving to a cooling rack, the cookies will appear slightly wet on top.
Enjoy and store: These cookies are better after they have cooled slightly and the interior has set. Store any leftovers in an airtight container for up to 4 days.