To make the crust: Grease a 13 by 9-inch metal baking pan, then line with foil, leaving a 2-inch overhang on both ends, and grease foil.
Follow recipe for basic butter cookies to make dough (do not chill), then press dough evenly onto bottom of baking pan, using plastic wrap on top to prevent dough from sticking to your fingers, and chill until firm, about 20 minutes.
While crust chills, put oven rack in middle position and preheat oven to 375 degrees F.
Bake crust until golden brown, about 30 minutes. Cool in pan on a rack 20 minutes. (Leave oven on.)
To make topping while crust cools: Cook sugar in a 2 1/2 to 3-quart heavy saucepan over moderate heat, undisturbed, until it begins to melt. Continue to cook, stirring occasionally with a fork, until sugar is melted to a deep golden caramel. Tilt pan and carefully pour in cream (caramel will harden and steam vigorously). Cook over moderately low heat, stirring, until caramel is dissolved. Remove from heat and stir in butter, vanilla, salt, and pecans.
Immediately spread topping over cooled crust and bake until bubbling, about 20 minutes. Cool completely in pan on rack, about 2 hours.
Run a heavy knife under hot water, then wipe dry and cut confection into 2-inch triangles, diamonds, or squares. Caramel pecan cookies keep, layered between sheets of waxed paper or parchment, in an airtight container at room temperature 1 week.
Whisk together flour, baking powder, and salt in a small bowl.
Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer (preferably fitted with paddle attachment) or 6 with a handheld. Beat in egg and vanilla. Reduce speed to low, then add flour mixture and mix until just combined.