Preheat your oven to 400 degrees Fahrenheit.

Warm 3/4 cup of apricot jam in a small saucepan over medium-low heat for 2 to 3 minutes, stirring occasionally, until it becomes loose and spreadable. You can also microwave it in a small bowl for 30 seconds.

While the jam is heating, in a large bowl, combine 1/4 cup granulated sugar, 1/4 cup brown sugar, 2 tablespoons flour, 1 1/2 teaspoons cinnamon, 1 teaspoon lemon juice, and a pinch of kosher salt.

Mix the dry ingredients together until well combined.

Add the sliced Granny Smith apples to the bowl and toss gently until every slice is evenly coated with the sugar mixture.

Lightly flour a clean countertop and roll out the puff pastry sheet into a rectangle about 9 by 13.5 inches. Transfer it to a parchment-lined baking sheet.

Using a sharp knife, score a border about 1 inch from the edge of the puff pastry, being careful not to cut all the way through. Prick the inner area of the pastry all over with a fork.

Spread 1/2 cup of the warmed apricot jam evenly over the inner area of the pastry, reserving the remaining 1/4 cup for later.

Arrange the apple slices in a single layer over the jam, overlapping them slightly for a beautiful presentation.

Fold the outer border of the pastry up and over the edges of the apples, pressing gently to seal. Brush the folded crust with the beaten egg and sprinkle with the remaining 1 tablespoon of granulated sugar.

Scatter the cold butter cubes over the apples.

Bake for 30 to 35 minutes, until the crust is deep golden brown and the apples are tender but not mushy.

Reheat the remaining 1/4 cup of apricot jam until loose, then brush it over the hot apples for a glossy finish.

Let the tart cool on the baking sheet for 5 to 10 minutes, then slice and serve warm with a scoop of vanilla ice cream.