Lightly butter an 8-inch (20 cm) square baking pan. Line it with parchment paper, leaving an overhang on two sides to form handles. Butter the parchment as well for easy removal and clean slicing.

Add the walnuts to a dry skillet over medium-low heat. Toast for 5–7 minutes, stirring occasionally, until fragrant and lightly browned. Let cool, then roughly chop and set aside.

In a medium to large heavy-bottomed saucepan, combine the packed light brown sugar, pure maple syrup, heavy cream, light corn syrup (if using), and fine sea salt. Stir gently over medium heat until the sugar dissolves and the mixture looks smooth and uniform.

Attach a candy thermometer to the side of the pan, making sure the tip does not touch the bottom. Bring the mixture to a gentle boil over medium heat without stirring. Continue boiling without stirring until the temperature reaches 236°F (113°C), the soft-ball stage, about 10–15 minutes. The mixture will thicken slightly and bubble steadily.

Remove the pan from the heat. Add the unsalted butter, vanilla extract, and maple extract (if using) on top of the hot mixture, but do not stir. Let the mixture cool undisturbed at room temperature until it reaches about 110°F (43°C), 20–30 minutes. The surface will look slightly dull and thicker; this cooling step helps prevent grainy fudge.

Once cooled, beat the mixture vigorously with a sturdy wooden spoon or heatproof spatula. Continue stirring until the fudge thickens and changes from glossy to matte, resembling thick frosting or peanut butter, 5–10 minutes. It should hold its shape when stirred.

Quickly fold the chopped toasted walnuts into the fudge until evenly distributed. Immediately scrape the mixture into the prepared pan and press into an even layer with a buttered spatula or the back of a buttered spoon, smoothing the top as desired.

Let the fudge cool at room temperature until firm, 2–3 hours, or chill in the refrigerator for 1–1 1/2 hours to speed setting. Use the parchment handles to lift the fudge from the pan and transfer to a cutting board. Cut into about 36 1-inch squares with a sharp knife, wiping the blade between cuts for clean edges.

Serve immediately or transfer the fudge squares to an airtight container. Store at room temperature for up to 3–4 days in a cool, dry place, or refrigerate for up to 2 weeks. For longer storage, freeze for 2–3 months and thaw before serving.