Grease 2 baking sheets with butter or cooking spray.
In a medium bowl, sift together the flour, baking soda, and salt. Set aside.
In a large bowl, using an electric mixer, beat together the butter and brown sugar until well blended and fluffy.
Add the eggs and vanilla and beat until evenly incorporated.
Lightly beat in half of the flour mixture. Add the sour cream and beat until well blended.
Stir in the remaining flour mixture and a generous ¾ cup of the pecans until evenly incorporated.
Use a spoon, or coffee scoop, and drop the dough onto the baking sheets into evenly shaped mounds, spacing about 2½ inches apart.
Using a greased hand, pat down the cookies until flattened on top.
Bake the cookies for 9 to 12 minutes, or until lightly browned on the edges and barely firm when pressed in the center. Change the pans around half-way through baking to ensure even browning.
Transfer the sheet to a wire rack and let stand until the cookies firm up slightly, 1 to 2 minutes.
Using a spatula, carefully transfer the cookies to wire racks. Let cool completely.
MAKE THE FROSTING
In a medium-sized saucepan, melt the butter over medium-high heat. Bring to a boil and gently simmer, stirring occasionally, until very fragrant and turns slightly golden, about 3 minutes, watch closely...don't let it burn!
Stir in the brown sugar and cook, stirring, for 1 minute more. Stir in 2½ tbsp hot wat and the corn syrup until the mixture is well blended and the sugar dissolves.
Vigorously stir in the powdered sugar and vanilla until well blended and completely smooth. Set the frosting aside, stirring occasionally, until it cools and stiffen just enough to spread, 2 to 4 minutes.
FINISHING THE COOKIES
Set the wire racks with the cookies over was paper to catch drippings. Using a small, wide-bladed spatula, spreader, or table knife, generously swirl the cookie tops with the frosting.
Sprinkle a few of the remaining pecans over the top of each cookie before the frosting sets.
Store in a single layer or layered with wax paper in an airtight container for up to 1 week of freeze for up to 1 month.
Notes
If at any point the frosting stiffens too much to spread, stir in jst enough hot water to make it spreadable.