Line a large baking sheet with parchment paper and set it aside.
In a medium, heavy-bottomed saucepan, combine the granulated sugar, brown sugar, evaporated milk, and butter. Cook over medium heat, stirring constantly with a wooden spoon, until the butter melts and the sugars completely dissolve, about 5 to 7 minutes.
Stop stirring and bring the mixture to a boil. Attach a candy thermometer to the side of the pan. Continue to cook, without stirring, until the thermometer reads 236°F (soft-ball stage), which should take about 8 to 10 minutes. The mixture will be bubbling and will have thickened slightly.
Immediately remove the saucepan from the heat. Carefully stir in the toasted pecans, vanilla extract, and salt. Continue to stir vigorously for 1 to 2 minutes; the mixture will become cloudy and begin to thicken and lose its gloss.
Working quickly, drop heaping tablespoonfuls of the mixture onto the prepared parchment paper, spacing them about 3 inches apart. Let the pralines cool completely at room temperature until they are firm and no longer sticky to the touch, about 30 minutes.