On a lightly floured piece of parchment, roll dough into an 11-inch round. Fit into a 9-inch tart pan with a removable bottom; tuck in edges. Prick bottom evenly with a fork; freeze until firm, about 20 minutes.

Preheat oven to 400 degrees. Line crust with parchment; fill with dried beans or pie weights. Bake on a rimmed baking sheet until edges are just starting to turn golden, about 20 minutes. Remove paper and beans; bake until bottom is golden and dry, 15 to 17 minutes. Let cool completely.

Reduce oven to 375 degrees. In a skillet, melt butter over medium heat. Add shallot; cook, stirring, until softened and translucent, about 5 minutes. Add cauliflower, 1/2 cup water, and cream; bring to a simmer, then cover and cook until cauliflower is very tender, 8 to 10 minutes. Remove from heat; season with 1/2 teaspoon salt and 1/8 teaspoon pepper. Let cool slightly.

Puree cauliflower mixture in a blender until smooth. Add egg; process until smooth. Stir in thyme. (You should have 1 1/2 cups puree.) Transfer to crust; smooth top with a spatula.

Toss radishes with oil; season with salt and pepper. Arrange on top of puree, slightly overlapping them in a circular pattern, covering surface. Bake tart on a baking sheet until radishes are beginning to shrivel and filling is bubbling around edges, about 45 minutes. Let cool completely before serving.