Combine the cream cheese with the red onion, chives, dill, green onions, carrot, celery and garlic in the bowl of a food processor. Pulse until mixed together and the spread reaches the consistency you want.
On 4 slices of bread, top one side of each with 2 tablespoons of the mixture. Top each with another slice of bread. Spread the tops of the second round of bread slices with 2 tablespoons more of the garden spread, then top with the remaining bread slices. Wrap the sandwiches and refrigerate for 1 hour.
When ready to serve, cut off the crusts, then cut each sandwich into 3 even fingers or 4 triangles.