Beat the butter and sugar until fluffy, about 2 minutes. Beat in the vanilla, then mix in the flour and salt just until combined. Fold in the toffee bits.

Divide the dough in half. Roll each half into a log about 2 inches wide, wrap in plastic, and chill until firm, at least 30 minutes.

Preheat the oven to 350°F. Slice the logs into 1/4-inch rounds and place them on parchment-lined baking sheets. Bake for 12 to 14 minutes, until the edges are lightly golden.

Let the cookies rest on the sheet for 5 minutes, then move them to a wire rack to cool completely.