Heat oven to 350°. Line two cookie sheets with parchment paper or silicone baking mats.
Beat brown sugar, butter, egg, and vanilla at medium speed (using a hand or stand mixer) until creamy. Reduce speed to low; add flour, baking powder, and salt. Beat until well mixed.
Shape dough into 2 tablespoon balls. Place 2 inches apart onto parchment lined cookie sheets. Make an indentation in each cookie with your thumb or the back of a wooden spoon, rotate it to hollow the cookie out slightly.
Make the filling: stir pecans, brown sugar, salt, and vanilla. Add 2 tablespoons whipping cream or milk. Stir until thick mixture forms, adding a bit more cream or milk as necessary. (If you use milk, you'll need only about 2 tablespoons. If you use cream you might need more.) It should be too wet, just a thick mixture.
Scoop about 1 rounded teaspoon of mixture into the center of each cookie. Chill 20 minutes.
Bake for 10-12 minutes, or until the cookies are baked and just starting to turn golden. Cool slightly before removing from cookie sheet.
Store in an airtight container for up to three days or freeze for up to one month.