Preheat the oven to 325° Fahrenheit. Grease a 10-inch tart pan with butter or cooking spray, then set aside. First, make the crust. Blitz up the unsalted, unroasted pistachios until they resemble flour, then mix the 1 1/4 cup ground pistachios with the arrowroot starch, 1-1 flour mix, sugar, and salt. Cut the chilled butter into cubes and knead the butter into the dry ingredients with your hands (or use a food processor) until the mixture comes together into a ball. Add the 1 egg yolk and mix together until fully combined. Press the crust mixture into the tart pan, evenly covering the bottom and sides. Bake tart for 15 minutes, then let cool completely before filling.
While the crust is cooling, make the filling. In a large bowl, using an electric mixer, beat together all of the filling ingredients until smooth and creamy. Once the crust is completely cool, pour the filling into the crust and bake for 30 minutes or until the filling is firm and does not jiggle. Remove from oven and let cool completely.
While the tart is baking, make the topping! In a medium saucepan or a large frying pan, heat the chopped strawberries, the sifted freeze dried raspberry powder (so no seeds remain), lemon juice, sugar, and rose water. Cook on medium low heat, constantly stirring, until strawberries release juices and the liquid cooks down/becomes thicker (about five minutes. Lower heat to a simmer, then mix the cornstarch and water in a small cup or bowl, and pour into the pan. Turn up heat to medium high and stir quickly until juices become thicker. Remove from heat and let cool completely.
Once tart and topping are cooled, spoon the strawberry compote on top of the cheesecake filling and spread to the edges (it will be a fairly thick layer) - you can also wait to spoon the topping onto each slice once the cheesecake is served! If you're going for overall presentation, spoon over the full tart, then slice extra strawberries thinly and layer on top as pictured. Remove from tart pan carefully (crust will be a bit fragile and may stick - use toothpicks to poke around edges), plate, and chill or freeze until ready to serve!