Combine yogurt, honey, and vanilla in a bowl; cover and chill.
Combine brown sugar, butter, and cinnamon in a large skillet; cook over medium heat until butter melts, stirring constantly. Remove from heat, and dip peach halves in mixture; set peach halves aside.
Return pan with butter mixture to heat; cook over medium-low heat 1 minute or until syrupy and bubbly, stirring often. Remove from heat; stir in oats. Spread mixture onto parchment paper, and cool 10 to 15 minutes. Break into pieces.
Place peach halves on grill rack; grill, cut sides down, 2 minutes. Turn and grill 3 minutes or until tender. Place peach halves on plates; top evenly with yogurt mixture, oat mixture, and walnuts.