In a mixing bowl, beat the egg whites, cream of tartar and salt until soft peaks form. Gradually add sugar, 1 tablespoon at a time, beating on high until stiff peaks form. Beat in extracts.
Shape or mold the 12-inch place of parchment paper over the outside of the 6-inch bowl. Invert bowl onto parchment paper-lined baking sheet. Secure paper edges by tucking between bowl and sheet.
Cut a small hole in the corner of pastry or plastic bag; insert basket-weave tip. Fill bag with meringue.
Begin the first vertical line by overlapping the edge of the paper-covered bowl base by 1/2 inch and pipe meringue down toward the baking sheet. Working from the top of the inverted bowl, cover the vertical line with 1-1/2-inch horizontal lines, leaving 1/2 inch between each.
Pipe another vertical line to the right of the first vertical line, overlapping ends of horizontal lines. Starting to the right of the first vertical line, pipe 1-1/2-inch horizontal lines over the second vertical line to fill in the open spaces. Repeat process until entire bowl is covered with basket-weave design.
Pipe a meringue coil pattern on top of the bottom of the bowl to form the basket's base. Bake basket at 225° for 2 hours.
Turn oven off and leave the basket in the oven for 1 hour. Remove from oven; remove bowl. Trim paper 1 inch below the top edge or very carefully remove paper.
Store basket in an airtight container for up to 3 days.