Try this for the creamy-smooth consistency of many classic cheesecakes. The strawberries add a splash of color. If you prefer, simply slice them or another fruit, such as peaches, or use a different berry, and spoon over individual servings.
Combine the first 4 ingredients in a bowl. Add the butter, combining with a fork, then use fingers to rub ingredients together to make a uniform crumb. Sprinkle with 2 teaspoons of water, then blend again briefly until mixture is somewhat clumpy. Add another teaspoon of water, if necessary.
Press crust evenly across the bottom of a 9-inch springform pan and about ½ inch up the sides. Refrigerate for 15 minutes.
Preheat oven to 350 degrees F.
Bake the crust for 8 minutes. Transfer to a rack and cool. When the pan has cooled, lightly butter the sides.
Set oven temperature to 300 degrees F.
Using an electric mixer (preferably a large stand model), blend the cream cheese on medium until smooth, scraping down the sides of the bowl several times. Add the sugar, about a third at a time, mixing thoroughly after each addition. Be careful not to overbeat; you don’t want to beat air into the cake. In a separate bowl, whisk the eggs and yolk until blended. Add the eggs, one half-portion at a time, to the cream cheese mixture and beat until smooth. Add the cream, sour cream, vanilla, and lemon extract and beat until evenly combined, scraping down the sides of the bowl.
Pour the batter over the crust. Place the pan in the center of a 16-inch-long piece of aluminum foil. Fold the foil snugly up and around the sides of the pan. Bake on the center oven rack for 55 to 65 minutes. Do not open the oven door at any point during the baking! When done, the cake will be higher at the edges than in the center, and the top (except the center) will have a dull (not shiny) finish. Turn off the heat, crack open the oven door, and let the cake cool for 1 hour. Remove the cake from the oven and cool to room temperature. Cover with foil and refrigerate the cake overnight.
Put the strawberry preserves into a bowl and stir briskly to smooth. Spoon about ⅓ cup of the preserves onto the cake, smoothing to cover. On top, arrange sliced berries, cut side down; brush the remaining preserves over the berries to make them glisten.
Remove cheesecake from the pan, slice, and serve.