In a large heavy bottomed saucepan bring the broth to a simmer. Add the mushrooms, cover and allow the mushrooms to cook for about 5 minutes, then use a slotted spoon to remove the mushrooms to a plate. Keep the broth warm over very low heat.
Put the butter and olive oil in a separate large saucepan over medium heat. When the butter is melted, add the mushrooms and garlic and cook until the mushrooms are tender and the liquid has evaporated - about 5 minutes.
Increase the heat slightly and stir in the rice. Allow it to toast for a few minutes, stirring it almost constantly.
Add the wine and stir and cook until the liquid is absorbed - about 2 minutes. Add 1 cup of the reserved broth and simmer until the liquid is absorbed (stirring very often). Continue to cook until the rice is just tender and creamy - adding more broth by the cupful and stirring often. It should take about 25 minutes.
When you've removed the risotto from heat, season generously with salt and pepper, then stir in the Parmesan. Allow the rice to come to room temperature, then stir in the beaten egg and put in the fridge to chill - for at least 1 hour.
for the filling:
Heat olive oil in a medium skillet over medium heat. Add the onion and cook until soft - about 4 minutes. Add the garlic and cook for another minute or two.
Stir in the beef, increase the heat some and cook until browned. Add the tomato paste and cook for an additional minute or two. Stir in the diced tomatoes and peas and season with salt and pepper. Reduce the heat and simmer for about 15 minutes - stirring often. Allow to cool.
When the risotto is cold, you can start forming the balls. You might want to be near your sink, so you can wet your hands often.
Scoop up a handful of the risotto and form it into a tight ball, squeezing out as much air as possible. Use your thumb to make a deep indention in the side of the ball and spoon about 1 tablespoon of the meat mixture in, with a cube of cheese. Use a bit more risotto to cover up the hole, and smooth it into a ball shape again. Keep repeating this process until you've used all the risotto, then put the balls in the fridge to firm up for about 30 minutes.
Have your beaten eggs in a shallow dish, and the breadcrumbs in another. Dredge each ball in the egg, then roll in the breadcrumbs.
Cook in hot oil until browned and crispy on all sides - about 5 to 6 minutes. Remove to a paper towel lined plate to drain.