Macerate the fruit: in a large bowl, toss sliced peaches and strawberries with sugar, salt, lemon zest, and basil. Cover and place in the fridge for at least 2 hours - but up to 3 days.
Preheat the oven to 350°F (175°C).
Meanwhile, brown the butter: heat the butter in a saucepan over medium until foaming. Add in the sesame seeds, stirring often, continuing to heat as the milk solids brown and the butter turns to an amber color. Set aside and allow it cool.
Make the topping: in a medium bowl, add the flour, oats, brown sugar, salt, and cinnamon. Mix to combine. Add the cooled brown butter (still liquid) and toss until clumps form. Set aside in the fridge until ready to use.
Strain off the syrup: place a strainer over a medium bowl. Pour the macerated fruits into the strainer, pressing to get as much juice as possible. Remove the basil leaves (keep them for the syrup) and discard the lemon peel. Set aside.
Cook the syrup: add the strained syrup to a saucepan along with the basil leaves. Simmer over medium heat until reduced to half. Remove from heat and set aside. Discard the basil leaves.
Whisk the cornstarch with 4 tbsp water to make a slurry. Mix into the syrup along with the macerated fruit.
Pour the filling into an 8-inch baking dish and cover with the topping. Sprinkle with slivered almonds. Bake for 40 minutes, or until the filling is bubbling and the crumble is golden.
Cool completely before slicing. Serve.