Mushroom and Swiss Wellington Pie

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3 tablespoons olive oil

One 2 1/2-pound chuck pot roast, cut into 6 wedges (try to find a round-ish one!) 

Kosher salt and black pepper

3 cloves garlic, minced 

3 shallots, finely diced 

1 1/2 teaspoons minced fresh thyme 

1 1/2 teaspoons minced fresh parsley 

1 pound sliced cremini mushrooms 

1/4 cup dry red wine 

3 tablespoons Dijon mustard 

2 tablespoons instant flour, such as Wondra 

6 slices Swiss cheese 

1 sheet frozen puff pastry, thawed 

1 egg whisked with 1 teaspoon water 

Sliced chives, for garnish