In a large frying pan (12-inch is ideal here) over medium-high heat, heat half (3 tablespoons) of the olive oil. Once it’s very hot, add half the mushrooms but don’t move them yet. Give them 1 to 2 minutes to brown underneath before adding 1/2 teaspoon kosher salt, a few grinds of black pepper, and half the garlic, then move them around, trying to get them to brown on more sides until they begin releasing their liquid. Cook the mushrooms, stirring, until the liquid mostly, but not fully, cooks off — a thin puddle should remain. Scrape these mushrooms into a large bowl and repeat the process with the remaining olive oil, mushrooms, garlic, plus more salt and pepper.
Once the second half of the mushrooms have mostly cooked off their liquid, add everything in the pan to the first half of mushrooms in the bowl. Add the cream cheese and stir just until combined. Then add half of the panko, all of the gruyere, half of the parmesan (1/2 cup), and most of the parsley (reserve some for garnish) and stir to combine. Transfer to a 2-quart baking dish.
Combine the melted butter and remaining panko (1 cup) and parmesan (1/2 cup) in a bowl with a couple pinches of salt. Sprinkle over top of the mushrooms and bake until the breadcrumbs are light golden brown, 25 to 30 minutes.
Sprinkle with remaining parsley and serve immediately.
To make ahead: Transfer the mushroom mixture to a baking dish, cover with foil, and refrigerate until needed. When ready to cook, warm the mixture in the oven with the foil on for about 10 minutes, then add the breadcrumbs and bake for another 25 minutes until the crumbs are light golden brown.