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Step 1
Preheat the oven to 325 degrees F (165 degrees C). Butter a 9-inch springform pan well.
Step 2
Start the filling: Heat olive oil in a pan over medium-high heat. Saute peppers and onions with a large pinch of salt until onions just start to turn translucent, about 5 minutes. Stir in garlic and cook for 2 more minutes. Turn off heat and allow to cool to room temperature.
Step 3
While the pepper mixture is cooling, prepare the crust: Combine crushed cracker crumbs, dried Italian herbs, and melted butter in a mixing bowl. Stir until crumbs are coated.
Step 4
Transfer the buttered crumbs into the prepared springform pan and press down into an even layer. Set aside until needed.
Step 5
Continue the filling: Combine eggs, flour, kosher salt, black pepper, cayenne pepper, and sugar in a large mixing bowl and whisk until smooth. Add the creme fraiche, cream cheese, and Parmigiano-Reggiano cheese, and mix until smooth. Stir in parsley, tarragon, thyme, and cooled pepper mixture until evenly combined.
Step 6
Transfer cheese mixture into the prepared springform pan. Tap the pan gently to settle the contents and place on a baking sheet.
Step 7
Bake in the lower center of the preheated oven until a skewer poked into the center comes out clean, 60 to 75 minutes. Let cool in the pan for 30 minutes. Run a knife around the edges and carefully remove the ring.
Step 8
Cheesecake should be thoroughly chilled in the refrigerator before serving, about 2 hours. Cheesecake can be served at room temperature, but it will not have the classic smooth, firm cheesecake texture, and will be more like a very light cheese quiche.