Pre-heat oven to 350 degrees Fahrenheit.
For the berry mixture, start by mixing the sugar, dried lavender and lemon zest together. Use your fingertips to rub the lavender and zest into the sugar, set aside.
In a large bowl, add the blueberries, chopped peaches, cornstarch, lemon juice and vanilla paste. Add the infused sugar and give everything a good stir. Set aside while you make the topping.
For the biscuit topping, whisk whisk together the flour, ¼ cup sugar and baking powder. Add the cubed butter and use your fingertips to break up the butter into the flour until butter is about the sizes of peas.
Pour 1 ¼ heavy cream and vanilla extract into the flour mixture and stir to combine until it is one cohesive mixture. It will be thick and sticky.
Pour berry mixture into baking dish and use a large tablespoon to dollop biscuit topping all over the top. Brush biscuits with 2 tablespoons heavy cream. Mix ⅛ cup sugar with lavender together and top biscuits with the infused sugar.
Bake blueberry cobbler for 55 minutes to 1 hour until the fruit mixture is bubbling and biscuits are light golden brown.
Once done, remove from oven and let cool for at least 20 minutes. Serve as is or with ice cream.