Put garlic and heavy cream into a sauce pan and cook on low for about 45 minutes or however long it takes for the garlic to be easily mashed. Take off the fire and smush the garlic until it is a smooth creamy texture.
Let the mushed garlic in cream continue to cook on very low, then cut off all the stems from the mushroom and chop into tiny bits to keep in the mushroom filling. Put the mushroom tops on the side to be filled at the end. Start heating up the 2 Tbsp of olive oil in a large pan on medium level heat. Add in the mozzarella cheese, shallots, and the mushroom stem bits. Keep cooking until the they are all soft and by stirring sparingly which should take a few minutes.
Put the crushed almonds into the heavy cream/mashed garlic mix and add in the pesto, salt, black pepper and the shallot, mushroom and cheese mix.
Set the oven to heat to 450 degrees and prepare a baking sheet by oiling it up.
Get a large bowl and mix together the other teaspon of olive oil, vinegar, a bit of salt and pepper. Put the mushroom tops in this bowl and mix to give it a nice coating. Then put each mushroom seperated on to the baking sheet and fill with the filling mixture.
Bake right until it starts turning brown which is about 15 minutes max.