Pulse toasted hazelnuts and ¼ cup sugar together in food processor until finely ground; add flour and pulse to combine.
Beat together butter and remaining ¼ cup sugar with hand mixer on medium-high speed until pale and fluffy. Add eggs, 1 at a time, beating thoroughly after each addition. Add extracts and beat to combine. Reduce speed to low, add nut mixture and beat just until combined.
Spread frangipane in tart shell and top with prepared pears, maintaining the pears shape and fanning slices slightly. Bake until pears are golden and frangipane is puffed and golden brown, 30-40 minutes. Brush pears with apricot preserves and cool tart completely in pan on rack. Remove side of pan and slide tart off base onto serving plate. Serve with whipped cream or ice cream if desired.