Preheat the oven to 375 degrees F (190 degrees C).
For the shortbread: Line an 8-inch square baking pan with aluminum foil, making sure to leave several inches of overhang on each side to lift out the shortbread (or use a rectangular tart mold with removable bottom). Cream together the sugar and butter, using an electric mixer on medium speed, until light and fluffy, 1 to 2 minutes. Mix in the vanilla, and then the flour and salt. The dough will be crumbly, pea-size balls. Dust your fingers in flour, evenly distribute the crumbles throughout the dough, and then press evenly into the pan and the edges, forming a smooth dough. Refrigerate for 30 minutes. Bake until the shortbread is a nice golden brown, 20 to 25 minutes. Cool the crust completely in the pan set over a wire rack.
For the maple butter: Bring the maple syrup to a boil, without stirring, in a small high-sided saucepan over medium-high heat. Cook the syrup, lowering the heat to medium if it begins to foam up to the top of the pot, until a candy thermometer reaches 235 degrees F to 240 degrees F (113 to 116 degrees C), soft-ball stage, about 15 minutes. Place the saucepan in a basin or bowl of ice water. Let cool, without stirring, until the thermometer reads about 120 degrees F (50 degrees C), 20 to 30 minutes. Remove the saucepan from the water. Beat the syrup, using a hand-held electric mixer on medium-high speed, until creamy, light in color (like peanut butter) and thickened, about 5 minutes. Continue to stir the maple syrup using a wooden spoon until it has lightened a few more shades, lost some of its sheen and slowly oozes off the spoon. Spread the maple butter over the cooled crust. Top with the toasted pecans and gently press into the maple butter. Sprinkle with sea salt. Set the pan aside for 30 minutes so the maple butter can set. It will change from a shiny finish to a dull, matte finish. Gently lift out of the pan and cut into 24 pieces.