Line a large baking sheet with parchment paper and set aside.
In a 3-quart heavy-bottomed saucepan combine 2 cups unsalted butter (room temperature), 2 cups sugar, and 1 teaspoon salt. Heat over medium-low, stirring constantly until the butter and sugar have melted and the mixture is smooth.
Clip a candy thermometer to the side of the saucepan. Continue cooking over medium-low, stirring constantly, and bring the mixture to 300°F (hard-crack stage). This will take about 10–15 minutes; keep the heat moderate so it cooks steadily.
As soon as the mixture reaches 300°F, remove the pan from the heat and stir in 2 teaspoons vanilla extract. Immediately pour the hot toffee onto the prepared parchment-lined baking sheet. Tilt the sheet or use an offset spatula to spread the toffee evenly if needed.
Let the toffee cool undisturbed for 5 minutes so it firms slightly but is still soft.
Using a large kitchen knife, cut the soft toffee into squares. Press the knife down along the lines a few times to ensure clean cuts and to prevent the toffee from fusing back together. Do not separate the pieces yet.
Let the scored toffee finish cooling until fully firm. To speed this, refrigerate the tray for 20–30 minutes if desired. Once fully cooled, break the toffee into individual pieces along the scored lines.
Melt 4 cups white melting wafers or candy chocolate according to the package directions, keeping the chocolate smooth and warm for dipping.
In a shallow dish or pie pan, combine ½ cup sugar and 1 tablespoon ground cinnamon to make the churro sugar.
Dip each piece of toffee into the melted white chocolate, allowing excess chocolate to drip off. Use tongs or clean fingers to handle the pieces.
After dipping, immediately place the chocolate-coated toffee into the cinnamon-sugar mixture and turn to coat all sides. Place the coated pieces on a clean piece of parchment.
Let the chocolate set completely, about 40 minutes at room temperature (or until firm). Once set, the churro toffee is ready to serve.