Slice tops off 3 pts. strawberries and cut lengthwise into wedges. Toss with brown sugar and 1/2 tsp. lemon zest in a medium bowl. Let sit at room temperature until juicy, about 20 minutes, or chill 2 hours.
Meanwhile, whisk cream and powdered sugar in a bowl until stiff peaks form. Fold in remaining 1/2 tsp. zest and the yogurt. Cover and chill until used, up to 2 hours.
Divide half of strawberry mixture among 6 parfait glasses. Top with half of cream mixture, dividing equally. Repeat layering and garnish with strawberry halves.