For the crust: Place the graham crackers and brown sugar in the bowl of a food processor. Process until finely ground, about 1 minute. With the processor running, slowly pour in the melted butter. Process the mixture until it is the texture of coarse sand. Transfer to an 8-inch springform pan. Using a measuring cup, press the crust into the bottom of the springform pan and up the sides, about 2 ½ inches. Press firmly to pack and make an evenly thick crust. Place in the freezer for 20 minutes. For the filling: In the bowl of a stand mixer with a paddle attachment, beat the cream cheese until softened and smooth. Scrape down the sides of the bowl and add the granulated sugar; beat to combine. Add the confectioner’s sugar, lemon juice, lemon zest, and sour cream. Beat to combine until very smooth, scraping the sides and bottom of the bowl as needed.  In a medium bowl, combine the heavy cream and vanilla extract. Using a hand mixer with a whisk attachment (or in the bowl of a stand mixer fitted with a whisk attachment), whip on medium-high speed until stiff peaks form, about 4 minutes. Add one-third of the whipped cream to the cream cheese mixture and gently fold in with a rubber spatula until completely combined. (Scoop the mixture from the bottom of the bowl and fold over the top to combine the mixture, without letting all of the air out of the whipped cream). Add the remaining two-thirds of the whipped cream and continue to gently fold until completely combined. Remove the crust from the freezer and add the filling. Gently push into an even layer and smooth the top with the back of a spoon. Cover the pan with plastic wrap and refrigerate for at least 12 hours or up to overnight. Loosen the cheesecake from the springform pan. Garnish with lemon slices. Cut pieces with a warm knife and serve with a dollop of lemon curd or sweet strawberries, if desired.