1Heat oven to 275ºF. Cover cookie sheet with heavy brown paper or cooking parchment paper.
2In medium bowl, beat egg whites and cream of tartar with electric mixer on high speed until foamy. Beat in 3/4 cup sugar, 1 tablespoon at a time; continue beating until stiff and glossy. Do not underbeat. Fold in hazelnuts. Drop meringue by 1/3 cupfuls in 8 mounds onto paper. Shape into circles, building up sides.
3Bake meringues 1 hour. Turn off oven; leave meringues in oven with door closed 1 hour 30 minutes. Finish cooling at room temperature, about 2 hours.
4In 1-quart saucepan, melt butter and chocolate over low heat, stirring constantly. Stir in 3/4 cup sugar, the cocoa, half-and-half and salt. Heat slowly to boiling; do not stir. Remove from heat; stir in vanilla. Fill each meringue with scoop of ice cream. Serve with warm sauce.