Preheat the oven to 425°F (220°C).
Place the quartered red potatoes and whole garlic cloves in a large pot and cover with cold water. Add a pinch of salt and bring to a boil over high heat. Cook until the potatoes are tender, about 15 minutes.
While the potatoes cook, toss the sliced red bell pepper, yellow bell pepper, zucchini, and red onion with olive oil, Italian seasoning, salt, and pepper in a large bowl.
Spread the vegetables evenly on a baking sheet and roast in the preheated oven for 20-25 minutes, stirring halfway through, until tender and slightly caramelized.
Heat a large skillet over medium heat. Add the turkey sausage links and cook for 12-15 minutes, turning occasionally, until browned and cooked through.
Drain the potatoes and garlic and return them to the pot. Add the butter and milk, then mash until smooth. Season with salt and pepper to taste.
Divide the mashed potatoes among four plates. Arrange the roasted vegetables and turkey sausage links alongside the potatoes.
Garnish with chopped fresh parsley and serve immediately.