Preheat the oven to 375 degrees.
Arrange the raspberries on a parchment-lined baking sheet and roast in the oven for 15 minutes, shaking the pan once halfway through cooking, until soft and beginning to release their juices.
In a small saucepan, combine the sugar, lemon zest, basil, and 1 cup of water over medium heat. Bring to a simmer, then remove from the heat and set aside to steep for at least 10 minutes or up to an hour. Remove the basil leaves and discard.
Puree the raspberries with the basil simple syrup, lemon juice, and remaining water in a blender until smooth and frothy. Strain through a fine mesh sieve.
Taste and add more water as needed until your desired potency is reached - keeping in mind that adding ice to your glass will dilute the drink. (I like to keep mine more concentrated, in case I choose to mix it with vodka)
Transfer to a pitcher with ice, garnish with fresh basil leaves, and bottoms up!