Shepherd's Pie with Ground Beef

Ingredients

• 2 Tbs. unsalted butter
• 2 medium carrots, peeled and chopped fine
• 1 large onion, chopped fine
• 2 lbs. 85% lean ground beef
• Kosher salt
• freshly ground black pepper
• 5 Tbs. all-purpose flour
• 1 Tbs. tomato paste
• ¼ cup heavy cream
• 1¾ cups low-sodium chicken broth
• ¾ cups mild beer
• 2 Tbs. soy sauce
• 2 tsp. minced fresh thyme leaves
• 1 cup frozen peas
• 2½ lbs. russet potatoes, peeled and cut into 2-inch pieces
• 2 Tbs. unsalted butter, melted
• ⅓ cup heavy cream, warmed
• salt and pepper to taste
• 1 large egg, beaten