Preheat the oven to 350 degrees F. Line 1 or 2 baking trays with parchment paper and set aside. In a food processor, combine the flour, 1/4 cup sugar, baking powder, and salt and pulse to combine. Add the chilled butter and process just until combined. With the motor running, add the cream through the feed tubes, stopping just before the dough forms a ball.

Turn the dough out onto a lightly floured surface and gently knead, forming a smooth ball. Do not overwork. Roll the dough out into a 3/4-inch thick round. Using a 3-inch cookie or biscuit cutter, cut out 7 circles. Knead the scraps together, roll, cut out 3 more circles.

Arrange the circles on the prepared baking trays, brush the tops with cream and sprinkle lightly with sugar. Bake for 25 to 30 minutes, or until the cakes are golden and firm to the touch. Cool on a rack.

Meanwhile, rinse and drain the strawberries. Cut each berry into thick slices and toss with sugar in a large mixing bowl. Add the lemon juice, kirsch, and orange zest, and gently mix. Set aside.

When ready to serve, split each shortcake in half and warm slightly. Place the bottom half of the shortcake on a dessert plate. Spoon about 1 cup of ice cream on the cake, arrange a scant cup of strawberries over and around the ice cream, and top with the remaining half of the cake. Serve immediately.

In a medium saucepan, bring the cream, milk, and vanilla bean to boil. In a large bowl, using a whisk or a rotary beater, whip the egg yolks. Gradually whisk in the sugar until thoroughly combined. Slowly whisk in the hot cream mixture and return to the saucepan. Over low heat, stirring constantly with a wooden spoon, cook until the mixture heavily coats the back of the spoon. Return to the bowl and cool over ice. Strain into a clean bowl and freeze in an ice-cream maker according to manufacturer's instructions. Scrape 1/2 of the ice cream into a large container and swirl 1 cup of the strawberry compote through. Repeat with the remaining half of the ice cream and another 1 cup compote. Freeze, covered, until needed.

In a 4-quart saucepan, combine strawberries, sugar, and lemon juice. Add the vanilla beans and cook over low heat until the liquid begins to thicken, about 45 minutes. Lower the heat and cook for 15 minutes more, stirring. Remove from the heat and cool.