- Make the dough: In the bowl of a stand mixer fitted with paddle attachment, gently cream butter, sugar, and vanilla bean paste on medium-low speed for 3 minutes. Add eggs one at a time, scraping sides of bowl after each egg is incorporated. Slowly add flour and salt until a stiff dough forms, about 1 minute. Turn dough out onto a lightly floured work surface and form into a disk or five disks for tartlets. Knead until smooth, about 2 to 3 minutes, then wrap and chill overnight.
- When ready to make the tart(s), place dough on a lightly floured work surface and roll out to the size of tart pan. Gently transfer dough to pan and press into edges. Prick dough with a fork, then place in freezer to chill for 2 hours.
- Preheat oven to 325 degrees. Bake until lightly golden brown, about 30 minutes, then set aside to cool while you prepare caramel.
- Make the caramel: In a medium saucepan, bring cream to a simmer. Turn off heat and add rosemary, then cover and set aside for 20 minutes. Strain cream into a bowl and set aside.
- In another medium saucepan fitted with candy thermometer, heat 1 cup of sugar over medium heat, whisking occasionally. When sugar begins to caramelize, whisk in another 4 tablespoons of sugar. Repeat until all the sugar has caramelized and turned golden brown. Remove from heat and very carefully add infused cream, whisking gently. (The cream will bubble very aggressively when added to sugar, so pour very slowly.) Whisk in butter and salt. Return pot to heat and cook until caramel reaches 248 degrees. Remove from heat and cool for 20 minutes.
- Assemble tart(s): Place a handful of toasted nuts into bottom of tart shell(s). Gently pour warm caramel over nuts, then set aside to cool at room temperature for 2 hours before serving.