Preheat oven to 375°F (190°C). Spray a tall-sided 10-inch fluted round removable-bottom tart pan with baking spray with flour.
On a lightly floured surface, roll Pâte Brisée into a 14-inch circle. Transfer to prepared pan, pressing into bottom and up sides. Trim edges, if necessary. Freeze until firm, about 20 minutes.
Top prepared crust with a piece of parchment paper. Add pie weights. Place on a baking sheet.
Bake until crust is mostly dry and set, 30 to 35 minutes. Carefully remove parchment and weights, and bake until inside of crust is dry and edges are starting to turn golden brown, about 5 minutes more. Reduce oven temperature to 325°F (170°C).
In a large skillet, heat olive oil over medium heat. Add artichoke and garlic, and cook for 1 minute. Add spinach, and cook until mostly wilted, about 1 minute. Transfer to a heatproof bowl, and let cool completely.
In a large bowl, whisk together cream, milk, eggs, salt, and white pepper until well combined.
In bottom of prepared crust, spread artichoke mixture, and sprinkle with cheese. Place tart pan on a rimmed baking sheet, and place in oven. Quickly but carefully pour cream mixture into crust.
Bake until filling is set and top is starting to turn golden brown, 55 minutes to 1 hour. Let cool completely in pan. Remove from pan before serving.