FOR THE CRUST: Adjust oven racks to upper-middle and lower-middle positions and heat oven to 325 degrees. Process cracker pieces and sugar in food processor until finely ground, about 30 seconds. Add flour and salt and pulse to combine, 2 pulses. Add 6 tablespoons melted butter and pulse until crumbs are evenly moistened, about 10 pulses. Brush bottom of 9-inch springform pan with 1/2 tablespoon melted butter. Using your hands, press crumb mixture evenly into pan bottom. Using flat bottom of measuring cup or ramekin, firmly pack crust into pan. Bake on lower-middle rack until fragrant and beginning to brown around edges, about 13 minutes. Transfer to rimmed baking sheet and set aside to cool completely. Reduce oven temperature to 200 degrees.
FOR THE FILLING: Using stand mixer fitted with paddle, beat cream cheese, 3/4 cup sugar, and salt at medium-low speed until combined, about 1 minute. Beat in remaining 3/4 cup sugar until combined, about 1 minute. Scrape beater and bowl well; add sour cream, lemon juice, and vanilla and beat at low speed until combined, about 1 minute. Add egg yolks and beat at medium-low speed until thoroughly combined, about 1 minute. Scrape bowl and beater. Add whole eggs two at a time, beating until thoroughly combined, about 30 seconds after each addition. Pour filling through fine-mesh strainer set in large bowl, pressing against strainer with rubber spatula or back of ladle to help filling pass through strainer.
Brush sides of springform pan with remaining 1/2 tablespoon melted butter. Pour filling into crust and set aside for 10 minutes to allow air bubbles to rise to top. Gently draw tines of fork across surface of cake to pop air bubbles that have risen to surface.
When oven thermometer reads 200 degrees, bake cheesecake on lower rack for 40 minutes. After 40 minutes, remove cake from oven and use toothpick to pierce any bubbles that have risen to surface. Return to oven and continue to bake until center registers 165 degrees, 2 1/4 to 2 3/4 hours longer. Remove cake from oven and increase oven temperature to 500 degrees.
When the oven reaches 500 degrees, bake cheesecake on upper rack until top is evenly browned, 2 to 4 minutes, placing rimmed baking sheet on lower rack to catch any drips. Let cool for 5 minutes; run paring knife between cheesecake and side of springform pan. Let cheesecake cool until barely warm, 2 1/2 to 3 hours. Wrap tightly in plastic wrap and refrigerate until cold and firmly set, at least 6 hours. (Leftovers can be refrigerated for up to 4 days.)
To unmold cheesecake, remove sides of pan. Slide thin metal spatula between crust and pan bottom to loosen, then slide cheesecake onto serving plate. Let cheesecake stand at room temperature for about 30 minutes. To slice, dip sharp knife in very hot water and wipe dry between cuts. Enjoy!
Try serving with fresh berries and whipped cream!
Recipe from America's Test Kitchen.