Heat the vegetable oil in a deep, heavy-bottomed saucepan until a breadcrumb sizzles and turns brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended!)
For the mushroom, dredge the Portobello mushroom in the flour to completely cover, then pat off any excess.
Dip the mushroom into the egg, until coated all over, then roll in the breadcrumbs.
Carefully place the mushroom into the hot oil and deep-fry for 3-4 minutes, until golden and crisp. Carefully remove with a slotted spoon and drain on kitchen towels.
To make the sauce, melt the butter with the olive oil in a frying pan over a medium heat. Add the garlic and cook for one minute.
Add the white wine and boil to reduce the liquid by half.
Add the double cream and simmer to reduce by half again.
To serve, place the mushroom in the centre of a warm plate and drizzle the sauce around.