1. In a 1- to 1 1/2-quart pan over medium heat, melt butter and stir often until golden brown, 5 to 7 minutes. Remove from heat.
2. Meanwhile, in a bowl, with a mixer on medium speed, beat sugar, flour, and dry mustard until well blended. Beat in prepared mustard and egg. Add hot butter in a thin, steady stream, beating until mixture is cool, 2 to 3 minutes. Gently stir in apples.
3. Spoon apple mixture into warm baked butter pastry and spread level. Sprinkle cheese streusel evenly over filling. Set tart on a foil-lined 12- by 15-inch baking sheet.
4. Bake in a 350° regular or convection oven until streusel is golden brown, 45 to 55 minutes. If tart edges brown excessively, drape lightly with foil. Cool on a rack about 1 1/2 hours. Remove pan rim. Cut tart into wedges.