Savory Tomato Bread Pudding

Name: Savory Tomato Bread Pudding
Ingredients: 2 pounds plum tomatoes , cored and cut into eighths; ½ cup extra-virgin olive oil , divided, plus extra for serving; 4 garlic cloves , minced; 2 teaspoons table salt , divided; 1½ teaspoons sugar; ¼–½ teaspoon red pepper flakes; 11 ounces baguette , torn into 1-inch pieces (about 10 cups); ½ teaspoon pepper , divided; 3 cups heavy cream; 1½ cups whole milk; 8 large egg yolks; 2 ounces Parmesan cheese , grated (1 cup), plus extra for serving; 2 teaspoons minced fresh thyme and/or rosemary