Preheat oven to 350°F. Melt butter over medium heat in a heavy-bottomed saucepan until frothy. Swirl pan frequently, watching for butter to turn from light yellow to dark golden brown and foam dissipates. Once butter has browned, immediately transfer to a large bowl and chill for 15 minutes, until cool but not solidified.
Meanwhile, whisk together flour, salt and baking soda. Set aside.
When butter is cool, whisk in molasses, Splenda Sweetener, egg and vanilla until smooth. Add prepared dry ingredients and mix using a spatula until only a few dry streaks of flour remain. Stir in the chocolate chips until just combined.
Scoop 12 1-tablespoon portions of dough onto ungreased baking sheet, leaving 1” between each portion. Bake on center rack for 8 to 10 minutes, or until cookies are lightly brown at the edges but still soft to the touch in the middle.
Let cookies cool on baking sheet for at least 5 minutes before transferring to a wire rack to finish cooling. Repeat with remaining dough.