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1
Preheat oven to 350 degrees F (175 degrees C).
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2
Whisk all-purpose flour, whole wheat flour, almond meal, 1 tablespoon sugar, lemon zest, and salt together in a large bowl. Cut in butter with a pastry blender until mixture is in pea-sized crumbles. Stir in buttermilk until dough comes together.
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3
Press dough evenly over the bottom and 1/2 inch up the sides of a 12x16-inch tart pan or sheet pan.
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4
Bake in the preheated oven until lightly browned, about 20 minutes. Place pan on a wire rack to cool completely, about 1 hour.
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5
Whisk egg yolks, 2/3 cup sugar, and cornstarch together in a heavy-bottomed pot. Whisk in milk. Add whole basil sprigs.
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6
Cook milk mixture over medium heat, whisking constantly, until mixture begins to steam, about 8 minutes. Reduce heat to low. Remove basil sprigs with tongs and discard. Whisk vigorously until custard thickens, about 1 minute.
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7
Set a wire mesh strainer over a large bowl. Pour custard into the strainer; use a rubber spatula to press it through the strainer into the bowl. Whisk vanilla extract into the custard. Press a piece of plastic wrap directly onto the surface. Refrigerate until cold, about 3 hours.
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8
Pour cooled custard over crust; spread evenly to edges of crust with a rubber spatula. Arrange apricot slices on top.
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9
Scoop apricot jam into a small microwave-safe bowl; microwave on high until melted, about 1 minute. Brush jam over apricot slices.
