Ham Pie

Ingredients

• 2 tablespoons vegetable oil
• 1 (14-ounce) package ham steak, diced
• 1 yellow onion, diced
• 1/2 teaspoon kosher salt, plus more, to taste
• 1/2 teaspoon ground black pepper, plus more, to taste
• 2 cloves garlic, minced
• 1 teaspoon fresh thyme leaves, chopped, plus more, optional, to taste, for garnish
• 2 tablespoons all-purpose flour
• 1 1/2 cups unsalted or low-sodium chicken stock
• 1 (16-ounce) package frozen peas and diced carrots
• 1 1/2 pounds russet potatoes, peeled and diced
• cold water, to taste
• 1/4 cup whole milk
• 2 tablespoons unsalted butter
• 3/4 cup sharp cheddar cheese, shredded
• 3/4 teaspoon kosher salt, plus more, to taste
• 1/4 teaspoon ground black pepper, plus more, to taste
• 1 egg yolk