The Easiest Brown Butter Tart Shell Ever
Position a rack in the center of the oven and preheat the oven to 400°F.
In a medium heatproof glass bowl, combine the butter, water, oil, sugar, and salt. Set the bowl directly on the oven rack and bake for 20 minutes, or until the mixture is boiling and the butter has started to brown.
Remove the bowl from the oven (but keep the oven on!), add flour all at once, and mix with a heatproof rubber spatula to combine. The dough is going to bubble and smoke-don't panic, this is what's supposed to happen! Mix until the dough pulls away from the sides of the bowl and looks a little bit like mashed potatoes, about 1 minute. Place the bowl on a wire rack and cool until the dough is still warm but can be handled, about 3 minutes.
Once cool, scoop 1 tablespoon of the dough into a small bowl. Place the remaining dough in an 8-inch round tart pan with a removable bottom. Use a tart tamper or your hands to press the dough evenly over the bottom and up the sides of the pan. Use a fork to poke holes all over the bottom and sides of the dough.
Bake for 15 minutes, or until the tart shell is golden brown. Cool completely on a wire rack before filling. While the tart shell is still warm, use the reserved 1 tablespoon dough to "spackle" any cracks. The tart shell can be stored at room temperature, under a cake dome or a large bowl turned upside down for up to 3 days.
Pour 3 to 4 inches of water into a medium, heavy-bottomed saucepan. Bring to a simmer over medium heat while you prep the ingredients.
In a medium heatproof glass bowl, whisk together the lemon juice, eggs, egg yolk, sugar, and salt. Place the bowl over the saucepan of simmering water (be sure the bottom of the bowl does not touch the water). Cook, whisking constantly, until the mixture becomes very thick and registers 170°F on an instant-read thermometer, 15 to 20 minutes.
Remove the bowl from the saucepan. Pour the mixture into a high-powered blender and let cool to 140°F before proceeding, 5 to 10 minutes. As you wait, chop the butter into 1 to 1 1/2-inch pieces.
Blend the cooled lemon mixture on medium, adding the butter through the blender's feed tube one or two pieces at a time, adding more butter only once the previous pieces have been fully incorporated and the mixture is smooth. Once all the butter has been added, use a rubber spatula to scrape the sides of the blender pitcher. Blend on high until pale yellow and smooth, about 30 seconds more.
Immediately pour the cream into the tart shell and use an offset spatula to smooth the top. Press a sheet of plastic wrap directly against the surface of the cream to prevent a skin from forming. Refrigerate for at least 4 hours, preferably overnight.
Remove the tart from the refrigerator and carefully peel off the plastic wrap. Use an offset spatula to smooth the surface of the lemon cream once more to remove any indentations left by the plastic wrap. Unmold the tart by setting the pan on top of a wide glass or mug and carefully pulling down the sides of the pan. Place the tart on a serving plate, garnish with the blueberries, and serve immediately. This tart is best the day it's assembled.