Preheat oven to 400°; add oil to a preheated skillet over medium to medium-high heat.
Saute pepper, celery, water chestnuts, and onion for 2-3 minutes.
While veggies are still a little crunchy, transfer to a bowl; to the bowl also add bean sprouts, crab, soy sauce, and thyme; combine well with a spoon.
Paint half a sheet of phyllo dough with melted butter and fold sheet in half, making almost a square.
Pile a few spoonfuls of filling 2 inches from the bottom of the sheet and leaving 2 inches at either side of sheet.
Fold bottom flap up and side edges in, then roll up and over until you reach the top of the sheet.
Your crab pastry will look like a spring roll; dab the edges and sides of your roll with melted butter and place seam-side down on a pastry sheet.
Assemble all and bake on center rack 15 minutes or until lightly golden all over.