Step 1 Stir together the black sesame seed paste and simple syrup in a small saucepan. Add about three-fourths cup water and stir to blend. The mixture should look like paint. You may need to add more or less water depending on the sesame paste used. Heat just until simmering around the edges. Stir in 1 tablespoon lemon juice.
Step 2 Add the gelatin sheets to a large bowl of cold water and let bloom 4 minutes. Remove the gelatin from the water and squeeze out excess water. Add the gelatin to the sesame seed paste mixture and stir until the gelatin dissolves completely.
Step 3Pour the mixture into a lightly oiled 8-inch glass loaf dish. Chill several hours or overnight until gelatin is set.
Step 4To make the sesame nougatine, combine sugar and 2 tablespoons water in a small saucepan. Bring to a boil over medium heat, occasionally brushing down the sides of the pan with room temperature water. Cook until the syrup turns amber color (hard-crack stage, 300 to 310 degrees), about 9 to 12 minutes. Stir in the sesame seeds.
Step 5Pour the caramel out onto a Silpat or parchment-lined cookie sheet, spreading the caramel out to about one-eighth-inch thick. Let cool to room temperature, about 10 minutes, then crack some of the nougatine into 5 small shards for garnishing and break the rest into small pieces with a heavy glass so the candy is broken, not crushed.
Step 6Muddle the raspberries with 1 to 1 1/2 tablespoons lemon juice. Add 1 tablespoon of water or more to give them a saucy consistency.
Step 7To serve, loosen the edges of the gelatin with a spatula. Invert it onto a flat tray and turn the top side up. Trim about a quarter-inch around the edges so all sides are square. Cut into 1-inch cubes (use a knife sprayed with cooking spray for easier cutting). Arrange 5 cubes on a plate. Garnish with a shard of nougatine and sprinkle broken nougatine and a drizzle of muddled raspberries.