Heat oven to 350° F. Butter an 8-inch square baking pan. Line with 2 crisscrossed pieces of parchment, buttering in between and leaving an overhang on all sides; butter the parchment.
Make the crust: In a food processor, combine the flour, butter, sugar, and salt; process until fine crumbs form. With floured fingers, press the dough into the prepared pan and bake until just beginning to brown, 25 to 30 minutes.
Meanwhile, make the filling: Spread the walnuts on a rimmed baking sheet and toast in oven, tossing occasionally, until fragrant, 6 to 8 minutes; coarsely chop. In a medium saucepan, combine the sugars, butter, maple syrup, corn syrup, and cream; bring to a boil. Reduce heat and simmer, stirring, until slightly thickened, 4 to 5 minutes. Stir in the walnuts and vanilla.