Start by preheating your oven to 350°F. Line two baking trays with parchment paper or silicone baking mats to prevent sticking and make cleanup easier.
In a large mixing bowl fitted with the paddle attachment (or using a hand mixer), combine 3/4 cup brown sugar, 1/2 cup granulated sugar, and the butter. Mix on low to medium speed for about 3 minutes until everything is well combined and creamy. This is your base for the cookies.
Once the butter and sugar mixture is smooth, add in the powdered sugar, oil, eggs, sour cream, and vanilla. Mix again on low speed, scraping down the sides of the bowl as needed to ensure everything is evenly incorporated.
In a separate, smaller bowl, whisk together the flour, 1 teaspoon of salt, and baking soda. This helps distribute the leavening agents evenly throughout the dough.
Gradually add the dry flour mixture to the butter mixture. Mix until the dough forms. Be careful not to overmix—stop as soon as it all comes together.
Scoop about 3 tablespoons of dough and roll it into a ball. Roll each ball in the remaining 1/4 cup of granulated sugar to coat the outside. Place the dough balls onto your prepared baking trays, leaving about 1/2 inch of space between each cookie.
Gently press the top of each cookie with the bottom of a glass or cup to flatten it slightly and create a small indentation in the center. This is where your topping will go later.
Bake the cookies in the preheated oven for 8 minutes. They should be soft but not too browned. Let the cookies cool on the tray completely before adding the topping.