Combine flour, sugar, and salt in the bowl of a stand mixer. Add butter. Using the paddle attachment, mix on low speed until butter is smaller than pea-size but not totally crumbly. Whisk egg yolk, cream, and vanilla in a small bowl and add to flour mixture. Blend just until dough comes together and is smooth.
Form dough into a disk. Wrap in plastic wrap and chill at least 2 hours and up to 4 days.
Preheat oven to 375°. Lightly butter a tart pan or pans. Roll dough out on a lightly floured surface until 1/4 to 1/8 in. thick. Roll dough onto rolling pin, then unroll over pan(s). Press dough flush against bottom, into bottom corners, and lastly up inside of pan(s). Use your thumb to brush dough even with rim. If you have any cracks or holes, you can patch with the extra dough left from the rim.
Lay a piece or pieces of parchment paper into pan(s) over dough, cutting to fit as needed. Fill parchment with dried beans or pie weights.
Bake tart shell(s) until edges are light golden brown, about 20 minutes. Carefully remove parchment with beans and transfer to a plate or bowl. Bake tart shell(s) until center looks dry and is starting to turn deep golden brown, about 15 minutes more. Let cool completely, then remove pan rim and fill shell.