Set a deep, wide pot over medium-high heat and add the olive oil. Once the oil is hot, add the onions, carrots and celery. Saute, stirring, until the vegetables are lightly caramelized, about 7 to 8 minutes. Add the leeks, ginger and garlic and saute, stirring occasionally for 1 minute. Add the tomato paste to the pan and cook until the vegetables are well coated about 2 to 3 minutes. Add the shrimp shells and heads to the pan and cook until the shells are pink and well caramelized, about 5 minutes. Deglaze the pan with the brandy and sake and ignite. Continue to cook the brandy and sake until nearly evaporated, about 1 minute. Remove the shells and heads. Add the chicken stock, bay leaf and thyme and bring to a boil then reduce to a simmer. Season with 2 teaspoons salt, 1/2 teaspoon white pepper and the paprika. Add the rice to the soup and cook until the rice is tender and beginning to burst, about 45 minutes. Use an immersion blender (or in small batches in a bar blender) to puree the soup and then strain through a fine mesh sieve into a clean pot. Return to a simmer and add the coconut milk and cayenne pepper. Heat through but do not allow the soup to boil after adding the coconut milk. Adjust the seasoning and serve while hot with the shrimp toast. Garnish with the cilantro leaves and green onion tops.
Combine the shrimp, egg, egg white, green onions, cilantro, garlic, salt and white pepper in a food processor and process until blended but still slightly chunky. Add the cream cheese and pulse until smooth and thick. Add the cream and pulse just until blended being careful not to over-process.
Spread 1/4 cup of the shrimp mixture on each slice of bread, spreading it to the edges and smoothing the top. The remainder can be used within 2 days or frozen for up to a month.
Heat the vegetable oil to 360 degrees F in a large deep skillet. Add the shrimp toast, in batches, coated side down, and fry until golden on first side, 2 to 2 1/2 minutes. Turn and cook until golden on the second side, about 1 1/2 minutes. Drain on paper towels.
To serve, cut each toast diagonally into quarters, and serve one quarter in each bowl of soup.