Preheat oven to 200C.
To make the horseradish butter, use a food processor to mix the horseradish,parsley,mustard,lemon juice and a pinch of white pepper for about 1 minute or until well combined. Add butter,and process a further 30 seconds or until just combined.
Roll butter mixture in sheets of baking paper into a log shape about 4 centimetres in diameter. Refrigerate until firm.
Season the beef with salt and pepper. Heat a heavy-based frying pan over high heat and add a splash of olive oil. Seal the beef fillet on all sides until browned. Cook in the oven for 10-15 minutes,or until desired doneness*. Allow to rest 10-15 minutes,before slicing.
For the lemon thyme oil, combine all ingredients together in bowl. Season to taste.
In a non-stick pan,heat half of the lemon thyme oil and add the mushrooms,stem side down. Cook for 3-4 minutes until golden. Turn over,and brush the insides of the mushrooms with the remaining lemon thyme oil and cook until the mushrooms are tender.
Serve beefsliced with a disc of the horseradish butter,and a grilled mushroom.
*Tip:Use a meat thermometer to cook the beef:for rare,rest it at about 52C. Make it 55C for medium rare and 60C for well done.