Preheat your oven to 350 degrees Fahrenheit and prepare two baking sheets. You can either grease them lightly or line them with parchment paper for easy cleanup.
In a bowl, sift together 2 3/4 cups of all-purpose flour and 1 teaspoon of baking soda. Add in 1/4 teaspoon of salt and set this mixture aside for later.
In a large mixing bowl, using an electric mixer, beat together 1 1/3 cups of packed light brown sugar and 1 cup of slightly softened unsalted butter until the mixture becomes light and fluffy. This process should take about 2 to 3 minutes.
Add the 2 large eggs one at a time, mixing well after each addition. Then, add the 1 1/2 teaspoons of vanilla extract and mix until combined. Make sure to scrape down the sides of the bowl to ensure everything is well mixed.
Next, lightly beat in half of the flour mixture. You want to mix until just combined. It’s okay if there are still a few lumps; we’ll take care of those soon!
Now, add in 2/3 cup of sour cream and beat until the mixture is blended well. The batter will become creamy and smooth.
Gradually add the remaining flour mixture, along with the 3/4 cup of chopped pecans, and beat until everything is well mixed. The dough should be thick and somewhat sticky.
Using a 1/8-cup measure or an ice cream scoop, drop dough in even mounds onto the prepared baking sheets, leaving about 2 1/2 inches between each cookie. Don’t forget to lightly flatten the tops using your hand or the back of a spoon.
Place one sheet in the upper third of the oven and bake for about 9 to 12 minutes. The edges should be turning light golden brown, while the center remains just barely firm. Once done, let the cookies cool on the pans for about 2 minutes before transferring them to wire racks to cool completely.
While the cookies are cooling, prepare the frosting. In a medium saucepan over medium-high heat, melt 8 tablespoons of unsalted butter. Allow it to simmer, stirring occasionally, until it turns slightly golden and smells fragrant, which should take about 3 minutes.
Stir in 1 cup of packed light brown sugar and cook for an additional minute while stirring. This will help create a smooth frosting base.
Next, stir in 2 1/2 tablespoons of hot water and 1 tablespoon of light corn syrup. Mix well until the sugar dissolves completely.
Finally, vigorously stir in 1 1/2 cups of sifted powdered sugar and the additional 1 teaspoon of vanilla extract until everything is completely smooth and well combined, adding 1/4 teaspoon of sea salt to balance the sweetness.
Frost the cookies while the frosting is still warm; sprinkle with additional chopped pecans before the frosting sets. Enjoy your delicious creation!