Preheat oven to 375F. Place cubed ham in a standard sized pie plate and set aside.
Heat 1 tbsp of butter in a medium saute pan over medium heat. Add onion, carrots and celery. Cook for 3 minutes. Add peas and ¼ tsp salt. Cook for another minute until peas have thawed and turned bright green. Add the vegetables to ham in pie plate and wipe saute pan clean and return to stove.
Add remaining butter and melt. Add flour in one addition, whisking constantly. Cook roux until smooth, about 2 minutes. It's ok if the flour browns slightly. Whisking constantly, add broth in two additions. Once incorporated, add milk. Cook liquid for 6-7 minutes, whisking constantly until it is very thick. Stir in dried thyme and remaining salt.
Pour liquid over top ham and vegetables in pie plate. Stir to combine. Working quickly, Cover with puff pastry, trim edges and cut some slits in the top to allow steam to release. The puff pastry will soften quickly, press edges to side of pie plate and crimp, if desired.
Bake in the centre of the oven for 40-45 minutes. Check halfway through and Cover with foil if browning too quickly.