Prepare Meringue Box: Preheat oven to 200 degrees F. Line 2 large cookie sheets (16 1/2" by 12 1/2" each) with parchment paper. With nontoxic pen, trace one 8" by 8" square and two 8 1/2" by 1 1/2" rectangles on each sheet of parchment. (If not using a nontoxic pen, turn parchment over so that tracing side does not touch food.)
In large bowl, with mixer on high speed, beat egg whites and cream of tartar until soft peaks form. Sprinkle in sugar, 2 tablespoons at a time, beating until sugar dissolves and meringue stands in stiff, glossy peaks when beaters are lifted.
Fit large decorating bag with large round tip (3/8-inch opening). Fill bag with half of meringue. To make sides of box, pipe meringue lengthwise in 3 side-by-side strips to fill one rectangle; repeat with remaining rectangles. With meringue remaining in decorating bag, pipe an outline around both 8-inch squares. Spoon half of meringue remaining in bowl into each square. To make bottom of box, spread meringue in 1 square for a flat base. To make top of box, with back of spoon, swirl meringue in other square to make puffy peaks.
Bake meringues on 2 oven racks 2 hours, rotating cookie sheets between upper and lower racks after 1 hour. Turn off oven; leave meringues in oven 1 hour or overnight to dry.
When meringue is dry, carefully remove pieces from parchment. If not assembling box right away, store in tightly sealed container at room temperature up to 2 weeks.
To assemble box: With serrated knife, trim base all around to make an even 7 1/2-inch square. Trim 2 box sides so that rectangles are each 7 1/2 inches long. Do not trim remaining 2 sides. Using melted white chocolate as glue, attach two 7 1/2-inch sides, flat sides in, to outside of square base, then attach remaining sides to base and adjacent sides. (If side pieces crack, you can glue them together with melted chocolate.) Use extra chocolate along inside seams to reinforce corners and prevent filling from leaking out later. Let box stand at room temperature at least 1 hour to allow chocolate to dry completely.
Prepare Amaretto Cream: In medium bowl, with mixer on medium speed, beat heavy cream with sugar until stiff peaks form. With rubber spatula, gently fold in amaretto; cover and refrigerate up to 4 hours if you like.
To serve, place meringue box on square platter or serving tray; spoon Amaretto Cream into box. Arrange some of fruit on top of cream; lean meringue top against side of box. (If not serving right away, cover box loosely and refrigerate up to 2 hours.) Use serrated knife to cut into pieces. Serve with remaining fruit.
Tips & Techniques Once you’ve made the outline for the bottom and two sides of the meringue box on one sheet of parchment, you’ll cut measuring time in half if you place the second parchment sheet over the first and trace the outline onto it for the top and remaining two sides.