In small microwave-safe bowl, melt butter. Mix in brown sugar, lemon juice, rum (or brandy or orange liqueur), cinnamon, ground cloves and nutmeg. Stir to dissolve sugar; set aside.
Place nectarine halves on grill, preheated to medium heat, skin-side down. Grill about 5 min., or until fruit begins to soften. Turn and grill cut sides of fruit, about 5 min., or until grill marks appear, then turn skin side down again, and brush tops generously with reserved glaze. Brush frequently while fruit grills to desired softness and edges of nectarines are lightly charred.
Serve drizzled with remaining glaze and scoops of vanilla ice cream, if desired.
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