Peel and cut the peaches into 1/4 - 1/8 inch slices. Sliver basil into ribbons. Place the sliced peaches in a saucepan and add sugar, basil, butter, flour and lemon juice. Cook over medium heat, stirring occasionally, for 20 minutes.
Butter a 9x9" baking pan, and pre-heat your oven to 350º.
While the peaches are cooking, make the crust. Mix the flour and powdered sugar (and salt, if you are using unsalted butter) in a medium to large bowl. Add the butter and mix with a hand mixer or by hand until the butter is incorporated and the mixture looks like course cornmeal. When you press the dough, it should just hold together. Spread the mixture in the bottom of a buttered 9x9" baking pan and press to form the crust. Bake crust at 350º for 15 minutes. Allow to cool at least 10 minutes.
While the crust is baking, mix the cream cheese and powdered sugar until smooth. Once the crust has cooled, use an off-set spatula or similar to spread the cream cheese mixture evenly over the crust.
Pour the peach mixture over the cream cheese-topped crust, and place in the oven. Bake at 350º for 30 minutes, or until peaches are bubbling and glossy. Cool completely before cutting.
