Preheat oven to 325 degrees F.
Coat a 9-inch springform pan with cooking spray. Wrap the outside of the pan with a double thickness of foil. Put a kettle of water on to boil for the water bath.
To make crust: Pulse vanilla wafers in a food processor into fine crumbs. Add oil and pulse to blend. Press crumb mixture evenly into bottom of prepared pan. (Rinse and dry the workbowl.)
To make filling: Process cottage cheese in food processor until very smooth and silky, stopping to scrape down the sides once or twice. Add cream cheese and process until smooth. Add 1 cup sugar, cornstarch, lemon juice, vanilla and salt; process until well blended. Add eggs and pulse several times just until mixed in. Sprinkle in lemon verbena (or lemon balm); mix with a rubber spatula. (Do not process.) Scrape the filling into the crust-lined pan.
Place the cheesecake in a shallow roasting pan and pour in enough boiling water to come 1 inch up the outside of the springform pan. Bake until the edges are set but the center quivers slightly, 50 to 55 minutes. Turn off the oven. Let the cheesecake cool in the oven, with the door ajar, for 1 hour.
Remove foil from pan. Cover cheesecake with plastic wrap and refrigerate until chilled, at least 2 hours.
To make topping: About 1/2 hour before serving, rinse strawberries. Set aside 3 whole berries for garnish; hull remaining berries and slice into a bowl. Sprinkle with 2 tablespoons sugar and toss to coat. Let stand until strawberries are juicy, 20 to 30 minutes.
To serve, place cheesecake on a serving platter and run a knife around the inside edge of the pan; remove pan rim. Make 3 lengthwise cuts in each whole berry; press lightly and arrange fanned berries in the center of the cheesecake. Garnish with a sprig of lemon verbena (or lemon balm). Cut cheesecake into slices and place on dessert plates. Top each serving with strawberries and juice and garnish with another lemon verbena (or lemon balm) sprig.