Preheat the oven to 200°F (95°C). Line a large rimmed baking sheet with foil. Set an oven-safe wire rack over it and lightly grease the rack with nonstick cooking spray. Measure the pretzels and vanilla and keep them ready. Prepare a second rack and tray if needed for space.
In a heavy 3- to 4-quart saucepan, combine the butter, granulated sugar, water and salt. Heat over medium-low heat, stirring steadily along the bottom, until melted and combined.
Continue cooking over medium-low heat, stirring gently, until the toffee reaches 305°F (152°C) on a candy thermometer. Keep the sensing tip in the mixture without touching the pan bottom. This can take about 15–20 minutes; use the temperature rather than the clock as your guide.
Remove the saucepan from the heat. Gently stir in the vanilla, then immediately add the pretzels. Turn them through the warm toffee with a sturdy heatproof utensil until coated.
Using small tongs, transfer the coated pretzels to the prepared rack, a few at a time. Space them in a single layer, separating touching pieces with utensils while the coating is warm. Let extra toffee drip onto the foil below.
Bake the pretzels on the rack at 200°F (95°C) for 20–30 minutes. Remove the tray and let the pretzels cool completely on the rack, allowing about 1 hour for cooling.
Once completely cool, leave the pretzels uncovered on the rack overnight, allowing about 8 hours to finish setting. Serve the firm, cooled pretzels in a bowl.