In a large Dutch oven or pot, melt butter over medium heat. Add the potatoes, carrot, and cabbage and cook, stirring, for about 5 minutes.

Add flour and cook, stirring, for 1 more minute.

Add chicken broth, milk, mustard, thyme leaves, and salt and pepper. Stir to combine.

Bring the mixture to a boil, then reduce heat to simmer. Simmer for 15-20 minutes, or until vegetables are tender.

Stir in corned beef and cheese and cook, stirring until cheese has melted. Taste and adjust seasoning as necessary. Remove from heat and allow to cool for 15-20 minutes.

Preheat oven to 425F and prepare a baking dish or individual dishes. Place on a baking sheet and spoon filling in.

Cut puff pastry sheets to fit your baking dish or dishes. Cut several slits in the middle to allow steam to vent. Combine egg with water and brush the tops of puff pastry pieces.

When filling has cooled sufficiently, place puff pastry pieces on top and bake in preheated oven for about 20 minutes, or until puff pastry is golden and filling is bubbling. Allow to stand 5 minutes before serving.