Oven Preparation: Initiate the preheating process of the oven to 350°F. Prepare two baking sheets by lining them with either parchment paper or a silicone baking mat.

Dry Ingredients Mixture: In a medium-sized mixing bowl, combine the all-purpose flour, salt, baking soda, and cream of tartar. Ensure thorough mixing.

Wet Ingredients Mixture: In a separate, larger bowl, blend the softened butter, vegetable oil, brown sugar, and powdered sugar until a uniform consistency is achieved. Subsequently, incorporate the egg, milk, and vanilla extract, ensuring they amalgamate effectively.

Dough Formation: Gradually introduce the previously mixed dry ingredients into the wet mixture. Stir until a cohesive dough forms.

Dough Shaping: Manually shape the dough into spheres roughly the size of a large golf ball. Position these on the prepared baking sheets, ensuring there's adequate space between each.

Creating Indentations: Utilizing a buttered measuring cup, gently form an indentation in the center of each cookie sphere.

Baking Process: Commit the cookies to the oven for a period of 8 to 10 minutes. Upon completion, the cookies should remain light in coloration. Allow them to cool on the baking sheet for 5 minutes before relocating them to a cooling rack.

Caramel Preparation: In a microwave-safe container, combine the caramels and milk. Microwave in 30-second intervals, stirring after each, until the caramels are fully melted. Integrate the salt into the melted caramel mixture.

Finalizing the Cookies: Carefully pour or drizzle the prepared caramel into the indentations of each cooled cookie. Immediately garnish with flaked sea salt. Ensure the caramel sets firmly before relocating the cookies.

Storage: Once the caramel has set, these cookies can be stored in an airtight container for a maximum of one week.