Combine the shrimp, egg, egg white, green onions, parsley, 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 onto each slice of bread, spreading to the edges and smoothing the top.
Heat the vegetable oil to 360 degrees F in large deep skillet. Add the shrimp toast in batches, coated sides down, and fry until golden on the 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. Serve hot, with a drizzle of duck sauce or a dab of pepper jelly, as desired.