For the Blanched Basil: Bring the water, ascorbic acid, and salt to a boil in a saucepan. Blanch the basil for 5 to 8 seconds, or until wilted. Make sure that the basil does not lose its color by letting it blanch too long.
Shock the basil in ice water and drain. Squeeze the excess water out of the basil.
Line a half sheet pan with a nonstick rubber mat. Place a 25cm / 10in by 38cm / 15in by 2cm / 1in Plexiglas or stainless steel frame inside the sheet pan.
For the Basil Jelly: Purée 195g / 6.88oz of the blanched basil, the water, ascorbic acid, and salt in a blender. Strain. Add sugar as needed; it should be sweet but not too sweet. Stir until the sugar is dissolved.
Bring 250g / 8.82oz of the basil mixture and the agar-agar to a boil in a saucepan over medium heat. Combine this with the rest of liquid off the heat and pour into the frame immediately. If the basil water sits in the hot pot for too long, it will turn brown.
Allow the mixture to set in the refrigerator, about 20 minutes.
Cut into rectangles 1cm / 0.5in by 7.5cm / 3in using a metallic cutter or knife. Slightly separate the jelly rectangles from one another and reserve covered on the nonstick rubber mat in the refrigerator.