Toast the pecans: Heat the oven to 350°F. Toast the pecans on a baking sheet for 6 to 8 minutes, until fragrant. Cool and finely chop. Leave the oven on if you are baking soon.
Make the dough: Beat butter and brown sugar until creamy, about 2 minutes. Beat in the egg yolk and vanilla. Mix in flour and salt just until combined.
Shape and chill: Scoop 24 approximately 1-tablespoon portions. Roll into balls and space 2 inches apart on parchment-lined baking sheets. Press a deep well into each, leaving the bottom intact. Repair any large cracks. Refrigerate for 30 minutes.
Cook the filling: In a small saucepan over medium-low heat, stir together butter, brown sugar, corn syrup, and cream until melted. Let the mixture bubble gently for about 1 minute, stirring. Remove from the heat. Stir in pecans, vanilla, and salt. Cool about 10 minutes, until thick and spoonable.
Fill and bake: Heat or maintain the oven at 350°F. Deepen wells if needed. Add about 1 teaspoon filling to each cookie, without overfilling. Bake one sheet at a time for 11 to 13 minutes, until the edges are set and lightly golden and the filling bubbles gently.
Cool: Leave on the pan for 10 minutes, then transfer to a rack. Cool completely before storing. Add a few flakes of sea salt while warm, if you like.
Recipe notes: Measure flour lightly or by weight. Pecans should be chopped small enough to sit inside the wells. Baking sheets and ovens vary, so use the appearance of the edges as your final cue.