1. Preheat oven to 350 degrees. Butter a 15-by-10-inch rimmed baking sheet, and line with parchment paper, leaving a 1-inch overhang on long sides; set aside. Spread nuts on another rimmed baking sheet. Toast until nuts are fragrant and lightly golden around the edges, about 10 minutes. Transfer nuts to a clean surface; spread evenly, and let cool completely. Coarsely chop, and set aside.

2. In the bowl of an electric mixer fitted with the paddle attachment, beat 2 sticks of butter with the brown sugar on medium speed until light and fluffy, about 3 minutes, scraping down the sides of the bowl as needed. With mixer on low speed, add flour and a pinch of salt; mix until just combined.

3. Transfer dough to prepared baking sheet, and cover with parchment paper. Using a wine bottle or small rolling pin, roll along the length of pan to smooth dough. (Alternatively, press the dough into the pan with the back of a large spoon.) Bake until lightly golden, 10 to 12 minutes. Transfer to a wire rack to cool completely.

4. Combine granulated sugar, cream of tartar, remaining 2 1/2 teaspoons salt, and 1 cup water in a wide, heavy-bottom saucepan. Cook over high heat, without stirring, until some sugar begins to melt and turn golden, 5 to 7 minutes. Reduce heat to medium; continue to cook, stirring occasionally with a wooden spoon, until sugar is completely melted, mixture is deep golden, and a candy thermometer registers 300 degrees (hard-crack stage). Stirring constantly, carefully pour cream slowly down the side of the pan (it will spatter) until fully combined. Remove from heat; add remaining 1/4 stick butter and stir to combine.Transfer caramel to a heatproof bowl to cool for 10 minutes.

5. Stir in nuts; spread caramel mixture over cooled crust. Bake until caramel is set, about 10 minutes. Transfer to a wire rack to cool. Cut into 3-by-2-inch bars. Bars can be kept in an airtight container at room temperature for up to 1 week.