Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper.
Sprinkle each half of squash with 1/4 tsp. salt, then place facedown on prepared sheet. Trim 1/4" from top of garlic head to expose cloves. Place head on a sheet of foil, drizzle oil over, then wrap tightly to enclose. Transfer to baking sheet. Bake until interior of squash is fork-tender and garlic is very soft, 30–50 minutes, depending on size of squash. Let cool slightly.
Carefully unwrap garlic. Let cool slightly, then squeeze pulp out onto a cutting board. Finely chop.
Heat cream cheese, milk, and chopped garlic in a medium saucepan over medium, stirring occasionally, until smooth. Season with salt and pepper; set aside.
Using a fork, scrape squash crosswise to pull strands from shells into a large bowl; reserve shells. Toss squash with cream cheese mixture, salami, spinach, tomatoes, Parmesan, red pepper flakes, if using, and 1 cup mozzarella until combined. Stuff squash mixture back into shells and top with remaining 1/2 cup mozzarella.
Transfer shells to oven and bake until squash mixture is bubbling and lightly browned, about 25 minutes.