Make the pastry: In a large bowl, beat together sugar and butter with a hand mixer on medium-high speed until light and fluffy, 1–2 minutes. Add 1 lightly beaten egg and beat until smooth. Add flour and salt and mix on low speed until a crumbly dough forms. Transfer to a lightly floured work surface and flatten dough into a disk; divide disk into 4 equal portions and flatten each portion into a disk. Working with 1 disk at a time, roll out to 1⁄8" thickness, transfer to a 6"-diameter 12-oz. tart tin, and transfer tin to a baking sheet; repeat with remaining disks and tins. Trim edges and lightly prick bottoms with tines of a fork; refrigerator for 1 hour.
Heat oven to 375°. Line each tin with a parchment paper circle and fill with dried beans or pie weights; bake until just set, 15 minutes. Remove weights and parchment and continue baking tart shells until the edges are golden brown, 12–15 minutes more. Transfer tins to a wire rack and let tart shells cool. Reduce oven temperature to 300°.
Make the filling: Heat cream, milk, nutmeg, and vanilla seeds in a 2-qt. saucepan over medium-high heat until it begins to simmer; remove from heat. In a large bowl, whisk together remaining eggs, brown sugar, and egg yolks until smooth. Slowly add warm cream mixture, whisking constantly until smooth. Place baking sheet with tart shells on oven rack and pour custard into shells; slide rack into oven and bake until custard is set but still slightly loose in the center, 30–35 minutes. Transfer tarts to a wire rack and let cool. Chill for at least 2 hours. To serve, garnish the tarts with grated nutmeg, halve or quarter the tarts, and serve them cold or at room temperature.