Preheat the oven to 450˚ F. In a small bowl combine 2 tablespoons of the olive oil with two thirds of the minced garlic. Scrape the gills from the inside of the mushroom caps. Set the mushroom caps on a baking pan, gill side up, and brush lightly with the garlic-oil mixture. Season with salt and pepper. Bake for 10 minutes.
Meanwhile, mix the filling. Combine the cream cheese, mayonnaise, remaining garlic, ½ teaspoon of the thyme, and the spinach in a medium bowl. Stir together until evenly blended. Gently stir in the artichokes. Season the mixture with salt and pepper to taste. Spoon the filling mixture over the roasted mushroom caps.
In another small bowl, combine the remaining 1 tablespoon of olive oil with the breadcrumbs, Parmesan, and remaining 1 teaspoon of thyme. Stir with a fork to blend. Sprinkle the breadcrumb mixture over the top of the filling mixture on each mushroom. Bake for 10 more minutes or until golden and warmed through. Serve immediately.