To make the sauce: In a small bowl, stir together the mustard and honey. Set aside.
Chop florets into small pieces or pulse lightly in food processor. Toss in a mixing bowl with shredded cheese. Set aside.
Beat egg and stir in the milk. Sift flour, baking powder, and salt together and combine them with the egg and milk mixture, beating well. Beat in 1/2 teaspoon oil as well. Pour mixture over broccoli and cheese and toss to coat well.
In a large skillet or saucepan heat oil to 375 degrees F (190 degrees C).
Drop broccoli mixture by spoonfuls into 375 degrees F (190 degrees C) oil and fry until golden brown. Serve with honey mustard sauce.