Grease several baking sheets, or spray with non-stick spray.
In a medium bowl, sift together the flour, baking soda, and salt: set aside.
In a large bowl, with an electric mixer on medium speed, 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 (if using), until evenly incorporated.
Using a heaping ⅛-cup measure, or a coffee scoop, drop the dough onto the baking sheet into evenly shaped mounds, spacing about 2 & ½ inches apart.
Using a greased hand (or fingers), pat down the cookies until flattened on top.
Bake the cookies, one sheet at a time, in the upper third of the oven for 9 to 12 minutes, until lightly browned at the edges and barely firm when pressed in the centers.
Reverse the sheet from front to back halfway 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 and let stand until cooled.
FOR THE FROSTING
In a medium saucepan, melt the butter over medium-high heat.
Bring to a boil and gently simmer, stirring occasionally, until it smells very fragrant and turns slightly golden, about 3 - 4 minutes; watch carefully!
Stir in the brown sugar and cook, stirring, for 1 minute more.
Stir in 2 & ½ tablespoons hot water 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 stiffens just enough to spread, about 2 minutes.
Using a spatula, or spreader, or table knife, generously swirl the cookie tops with the frosting.
If using, add a few chopped pecans on top of the frosted cookie, doing this for each cookie as you go...the frosting will begin to set.
(If the frosting stiffens too much, stir in just enough hot water to make it spreadable).
Store in a single layer, or layered with was paper in an airtight container.