In 5-quart Dutch oven, melt butter over medium-high heat until sizzling. Cook onions in butter 13 to 15 minutes, stirring frequently, until onions are light golden brown. Stir in garlic; cook 30 seconds. Sprinkle flour on onion mixture; cook and stir constantly 1 minute. Slowly stir in chicken stock. Heat to boiling; reduce heat to low. Cook uncovered 10 minutes, stirring occasionally.
Stir in cream cheese; stirring constantly with whisk until smooth. Stir in half-and-half until blended. Slowly add 2 cups of the cheese, 1/2 cup at a time, stirring constantly until cheese is melted. Stir in ham, 2 teaspoons of the Dijon mustard and the salt; cook 3 to 5 minutes or until heated through.
Meanwhile, set oven control to broil. Place French bread slices on ungreased cookie sheet. Spread remaining 1 teaspoon Dijon mustard evenly on cut sides of bread. Sprinkle evenly with remaining 1/2 cup cheese. Broil with tops 5 inches from heat 1 to 2 minutes or just until cheese is melted and golden brown. Watch carefully so cheese does not burn.
Serve soup topped with bread slices and cornichons.