Line an 8-inch square baking pan with aluminum foil that overhangs. Coat the foil with 1 tbsp of the butter.
In a 3-quart heavy-bottomed saucepan over low heat, cook the maple syrup, half-and-half, sugar, corn syrup, and salt until the sugar is dissolved (about 5 minutes), stirring constantly with a wooded spoon or heatproof spatula.
Bring he mixture to a boil over medium heat, then brush down the sides of the pan with a pastry brush dipped in water to prevent the sugar from crystallizing.
Place a candy thermometer in the pan and cook the mixture without stirring until it registers 238°F on the thermometer (about 15 minutes).
Remove the pan from the heat, remove the thermometer and place in warm water to cool it.
Sprinkle a marble board, or the back of a baking sheet with cold water, and immediately pour the hot mixture on the marble DO NOT SCRAPE THE BOTTOM OF THE PAN! (THIS CREATES HARD PARTS AND WILL THROW OFF THE CONSISTENCY OF THE WHOLE BATCH).
Dot the surface with remaining 3 tablespoons of butter. Let the mixture cool on the marble until it registers 110 F on the thermometer (about 5 minutes, or 15 minutes with a baking sheet).
Scrape the mixture into a stand mixer, add the vanilla, and with the paddle attachment, beat for 5-10 minutes until it looses its shine and thickens OR put in a bowl and use a wooden spoon.
Add chopped pecans, turn into prepared pan and use fingertips to even the top and press the fudge into the corners. Place the pan on a cooling rack and let set for 2 hours.