Preheat OvenPreheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
Mix Dry IngredientsIn a medium bowl, whisk together flour, salt, baking soda, and cream of tartar.
Blend Wet IngredientsIn a large bowl, cream together butter, vegetable oil, brown sugar, and powdered sugar. Add egg, milk, and vanilla extract, and mix well.
Form DoughGradually mix in the dry ingredients until a cohesive dough forms.
Shape CookiesRoll dough into golf ball-sized spheres. Place on baking sheets and press indentations into the center of each ball.
BakeBake for 8-10 minutes. Cool on the baking sheet for 5 minutes, then transfer to a wire rack.
Make Caramel ToppingMelt caramels with milk in the microwave, stirring until smooth. Mix in salt.
Assemble CookiesSpoon caramel into cookie indentations. Sprinkle with flaky sea salt.
Serve and StoreAllow caramel to set, then enjoy or store in an airtight container.