Classic Shepherd's Pie with Beef

Name: Classic Shepherd's Pie with Beef
Prep time: 25 min
Cook time: 25 min
Total time: 50 min
Cuisine: British
Ingredients: 1 Tbsp. vegetable oil; 1 small onion, finely chopped; 2 carrots, peeled and finely chopped; 2 cloves garlic, minced; 2 sprigs thyme or 1 tsp dried thyme; 1 and ½ lbs. ground beef chuck, or other medium fat ground beef; 1 tsp. salt; ½ tsp. pepper; 2 Tbsp. flour; 1 Tbsp. tomato paste; 1 cup beef broth (low sodium); 2 tsp. Worcestershire sauce; ¾ cup frozen corn, defrosted; ¾ cup frozen peas, defrosted; 2 ½ lbs. Russet potatoes, peeled and cut into 1/2-3/4 inch dice; 1 Tbsp. salt; 2 Tbsp. butter; ¼ cup milk, heated; 1 egg yolk