Slice yellow squash lengthwise to 1/4-inch thickness. Sprinkle with 1 teaspoon salt and set aside for at least 15 minutes.
Make the slaw:
In a medium bowl, combine oil, lemon juice, garlic, remaining 1/4 teaspoon salt, pepper, sugar(if using), and whisk until well blended. Add cabbage and toss until coated with dressing.
Make the cheese spread:
In a small bowl, combine goat cheese, cream cheese, and green onions with a spoon until thoroughly blended.
Assemble the sandwiches:
On a work surface, place 4 slices of bread and spread each with 2 tablespoons of the cheese mixture. Pat the squash slices dry with a paper towel and place them, the avocado, tomato, squash, red-cabbage slaw, and sprouts in layers on the prepared bread. Top each sandwich with a slice of the remaining bread, cut each sandwich in half, and serve.