Place the oven rack in the lower half of the oven and preheat to 325°F.
To make Crust - Using a food processor, pulse animal crackers until they are fine crumbs. Add in the sugar and pulse again. Add the butter in a steady stream and continue to pulse until the mixture starts to come together, about 10 1-second pulses. If you don't have a food processor or blender, simply crush crackers to fine crumbs and add sugar. Mix butter with hands until it comes together.
Transfer the crumb mixture to a 9-inch springform pan and press evenly into the bottom. Bake until golden brown, about 13-15 minutes. Remove from the oven and allow to cool. Once cool, wrap the pan with 2 18-inch pieces of foil. Set in a roasting pan and set aside.
To make Filling - place 1/4 cup of the sugar and the lemon zest in a food processor and process until the sugar turns yellow and fragrant. Add in the remaining sugar and pulse a few times to combine.
In the bowl of a stand mixer on low, beat cream cheese and add in the lemon sugar in a steady stream, then switch to medium and beat until creamy and smooth, about 3 minutes. Scrape down the sides of the bowl. Reduce the speed to medium-low and add the eggs, 2 at a time, scraping down the bowl in between additions. Add in the lemon juice, vanilla and salt and mix to combine. Pour in the cream and beat to combine, another 5 seconds. Scrape the bowl again to make sure everything has been incorporated and pour into the springform pan.
Place the pan in the oven and carefully add enough water to the roasting pan to make it halfway up the sides of the springform pan. Bake until the center is slightly giggly and the sides start to puff and the surface is no longer shiny, about 55 to 60 minutes. Turn off the oven and prop the oven door open with a towel or wooden spoon. Allow the cake to cool in the oven for 1 hour. Then cover and chill in the refrigerator before adding glaze.
Remove from the roasting pan and transfer to a wire rack. Run a small paring knife around the edges of the cake and let it sit at room temperature for 2 hours.
Lemon Glaze - In a small saucepan on low-medium heat, whisk together the eggs, lemon juice, sugar and lemon peel until blended. Add butter, whisking constantly until mixture is thickened and coats the back of a metal spoon. If desired, add food coloring. Transfer to a bowl and allow glaze to cool for 10 minutes. Place in refrigerator for 20 minutes to cool. Spread over cooled cheesecake and refrigerate for 24 before serving.