Heat oven to 400°F. Line a rimmed baking sheet with parchment paper.
Wipe the mushrooms clean with a damp paper towel. Remove the stems and chop them finely (about 3/4 cup). Arrange the caps hollow side up on the baking sheet.
Heat 1 tbsp olive oil in a skillet over medium heat. Add the chopped stems and garlic and cook 3-4 minutes, until the liquid cooks off. Stir in the panko and toast 1 minute. Scrape into a bowl and cool 5 minutes.
Stir the ricotta, Parmesan, parsley, lemon zest, salt, black pepper and red pepper flakes into the cooled stem mixture.
Brush the caps with the remaining 1 tbsp olive oil and sprinkle with a pinch of salt. Spoon a heaping 1 tbsp filling into each cap, mounding it slightly.
Bake 18-22 minutes, until the mushrooms are tender and the tops are golden. For a deeper brown top, broil 1-2 minutes.
Rest 5 minutes, scatter with parsley, and serve warm.