Combine water and salt in a saucepan. Bring to a boil and add rice. Reduce heat, cover, and simmer until rice has absorbed all the water, about 20 minutes. Remove from heat to cool; fluff with a fork.
Preheat oven to 300 degrees F (150 degrees C).
Pour cream and half-and-half into a saucepan. Scrape the vanilla bean seeds into cream mixture; add the bean pod. Bring mixture to a simmer; remove from heat. Remove and discard vanilla bean.
Whisk egg yolks and 1/3 cup sugar together in a bowl; gradually whisk in cream mixture. Fold rice into egg-cream mixture.
Pour mixture evenly into six 3/4-cup custard ramekins. Drop 6 raspberries into each ramekin. Place ramekins in a 9x13-inch baking pan; fill pan with water until halfway up the sides of ramekins.
Bake in the preheated oven until set in the middle, about 40 minutes. Remove ramekins from water bath and cool on a wire rack for 30 minutes. Cover ramekins with plastic wrap and refrigerate until completely chilled.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Arrange ramekins on a baking sheet; sprinkle each with 1 tablespoon sugar.
Broil in the preheated oven until sugar becomes golden brown, 3 to 5 minutes.