Preheat your oven to 400°F (200°C) and line a rimmed baking sheet with parchment paper.
Clean the portobello mushrooms by wiping the caps with a damp paper towel, then remove the stems and gently scrape out the dark gills using a spoon.
Heat the olive oil in a medium skillet over medium-high heat and add the ground turkey, breaking it into small crumbles as it browns.
Add the minced garlic, dried oregano, sea salt, and black pepper to the skillet, sautéing for about 1 minute until the garlic is fragrant.
Stir in the fresh spinach and cook just until it begins to wilt, then remove the skillet from the heat.
Place the mushroom caps on the prepared baking sheet with the hollow side facing up.
Divide the turkey and spinach mixture evenly between the two mushroom caps, pressing down slightly to pack the filling.
Sprinkle the crumbled feta cheese over the top of the turkey filling.
Roast in the oven for 15 to 18 minutes until the mushrooms are tender and the feta is slightly softened.
Remove from the oven and finish by drizzling the balsamic glaze over the mushrooms before serving.