Grease an 8-inch square baking pan with a thin layer of butter. Line it with parchment paper, leaving an overhang on two sides to help lift the fudge out later, then lightly butter the parchment as well to prevent sticking.

In a dry skillet over medium-low heat, toast the chopped walnuts for 4–5 minutes, stirring often, until they smell nutty and just deepen in color. Alternatively, toast in a 325°F (165°C) oven for 6–8 minutes. Set aside to cool.

In a heavy-bottomed medium saucepan, add the maple syrup, granulated sugar, heavy cream, butter, and salt. Stir gently with a wooden spoon or heatproof spatula to combine before turning on the heat so the sugar dissolves evenly.

Set the pan over medium heat. Stir occasionally as the mixture warms and the sugar melts. Once you see the first large bubbles and a steady boil, clip a candy thermometer to the side of the pot, making sure the tip does not touch the bottom.

Cook the mixture without stirring until it reaches 236–238°F (113–114°C), the soft-ball stage, usually 10–15 minutes. If you do not have a thermometer, drop a small amount of the hot syrup into a glass of very cold water: it should form a soft ball that flattens when you pinch it.

Remove the pan from the heat and set it on a trivet. Let the mixture cool undisturbed until it reaches about 110°F (43°C), or is just slightly warmer than body temperature. The surface will look thicker and less glossy. Do not stir during this cooling step.

When the mixture has cooled to around 110°F (43°C), add the vanilla extract and maple extract (if using). Stir just to combine. Adding them at this stage preserves their flavor.

Using a sturdy wooden spoon or a hand mixer on low speed, beat the mixture vigorously for 4–8 minutes, until it thickens, lightens in color, and loses its glossy shine. It should look like thick frosting and hold its shape. This beating step creates the classic creamy fudge texture.

Quickly fold the cooled, toasted walnuts into the fudge until evenly distributed. Work promptly, as the fudge will begin to set once it thickens.

Scrape the fudge into the prepared pan. Use a buttered spatula or offset spatula to spread it into an even layer, pressing gently into the corners and smoothing the top as much as possible.

Allow the fudge to cool at room temperature for 2–3 hours, or until completely firm. If your kitchen is very warm, you can move the pan to the refrigerator after the first hour, but slow cooling at room temperature gives the best texture.

Use the parchment overhang to lift the slab of fudge out of the pan onto a cutting board. Cut into approximately 1-inch squares with a sharp knife, wiping the blade with a warm damp cloth between cuts for the cleanest edges. Serve at room temperature.