Let goat cheese and cream cheese stand at room temperature for 30 minutes. Meanwhile, for garlic-rosemary oil, in a small saucepan combine olive oil, smashed garlic, and rosemary sprigs. Heat over medium-low to a gentle simmer; cook until garlic is golden (Be careful not to burn the garlic.) Remove from heat. Using a slotted spoon, remove garlic and rosemary from oil. Strip leaves from rosemary sprigs. Finely chop leaves and garlic; reserve for garnish.
For rosemary goat cheese, remove 2 tsp. zest and squeeze 1 Tbsp. juice from lemon. In a food processor combine goat cheese, cream cheese, 3 Tbsp of the garlic-rosemary oil, the lemon zest and juice, the 1 Tbsp. chopped fresh rosemary, ½ tsp. salt, and ¼ tsp. freshly ground black pepper. Process until smooth. Transfer to a bowl; cover and chill until ready to use (up to 3 days; let stand at room temperature 30 minutes before using).
Preheat oven to 425°F. In a large bowl combine squash, red onion, and ¼ cup of the garlic-rosemary oil; toss to coat. Add minced garlic, thyme leaves, the 1 tsp. chopped rosemary, and ½ tsp. each salt and pepper; toss to distribute evenly. Spread on a large-rimmed baking sheet.
Roast until squash is golden brown and crispy on the bottom, 30 minutes. Add chard leaves; toss to coat with some of the oil. Roast until leaves wilt, 5 minutes.
Spread rosemary goat cheese on a serving platter. Arrange roasted vegetables on top.
Drizzle with the remaining garlic-rosemary oil and top with the reserved chopped crispy garlic and rosemary. Serves 6.