Here I'm taking the confusion and fear out of making a pastry crust and baking a tart. Make this your go-to dessert, whether you're serving it at home to guests or taking it to a party. Everyone will love it.
Dough: Combine flour, sugar, and butter in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed until the butter and dry ingredients form a coarse cornmeal consistency, about 2 minutes. Alternatively, combine the flour, sugar, and butter in a large bowl and, with your fingertips or pastry cutter, crumble into a coarse cornmeal consistency.
Whisk the egg yolks and cream together in a small bowl and add to the flour mixture; mix on low until large chunks form. Turn the dough onto a flat, clean work surface dusted with flour. Press the dough with the heel of your hand and gather the pieces together to bring the dough into a ball. Knead the dough a few more minutes, form it into a disc, wrap tightly with plastic wrap, and chill for at least 1 hour and up to 3 days. This dough makes enough for two 10-inch tarts. (Note: The dough can also be frozen for up to 2 months. Before using, defrost overnight in the refrigerator.)
Line a baking sheet with parchment paper or silicon baking mat and butter the inside of the tart ring. Take the dough out of the refrigerator and cut it in half; reserve one half for later use. Cut the dough into large chunks. Pound the dough with a rolling pin and then knead it a few times to temper the dough to the consistency of Play-Doh. Dust your work surface and rolling pin with flour and pound the dough into a large disc, about ¼-inch thick. Roll the dough out to at least 2 inches larger than the ring to a thickness of 1/8 inch. Place the tart ring on top and trim the dough so that 2 inches remain around it. (Discard or reuse the excess dough scraps as cookie dough, etc.) Brush off the extra flour from the dough. Wrap the dough around the rolling pin and ease it into the tart ring. Dip the knuckle of your index finger in flour and press the dough into the crease with your knuckle so you have a straight edge, not sloping sides. Don'’t stretch the dough to fit, because it will shrink during baking. Roll your rolling pin over the top of the tart ring to neatly cut off the excess dough; pull off the trimmed dough and discard. Place the tart shell in the refrigerator to chill for at least 30 minutes and up to one day.
Custard: Whisk the eggs and sugar in a large bowl until smooth; then add the flour and whisk until thoroughly combined. Using a small, sharp knife, split the vanilla bean lengthwise; scrape out the pulp and seeds and smear them on the butter. Add the butter, vanilla pulp and seeds, and vanilla bean to a small, heavy-bottomed saucepan and heat over high heat until the butter is brown and foamy. Continue cooking the butter until it is dark brown and gives off a nutty aroma. Pour the butter in a slow, steady stream into the bowl with the egg yolks, whisking constantly. Remove vanilla bean. (Note: The filling can be prepared up to 10 days in advance and refrigerated in an airtight container. Just before using, bring it to room temperature until it is a spreadable consistency.)
Adjust the oven rack to the middle position and preheat to 350 F. Remove the prepared tart shell from the refrigerator. Spoon the filling about halfway up the tart and spread evenly. Sprinkle ½ cup berries on top of the custard. Bake the tart until the top is golden brown, about 30–40 minutes if you are using an 8-inch ring or 45 minutes if you are using a 10-inch ring. Remove the tart from the oven and allow it to cool completely, or for at least 2 hours.
To make the topping, set a colander inside a bowl; place 1½ cups blueberries into a second bowl. Bring sugar syrup to a boil, then pour over berries. Toss gently with a spoon to coat the berries, then immediately drain into the colander. To remove the tart from the baking sheet, slip a cardboard round under the crust and carefully slide the tart onto it, leaving the ring in place. Slide the tart onto a serving plate and remove the cardboard and the ring. Pile the blueberries on top of the tart. Immediately before serving, dust with confectioners sugar.