Soak sun-dried tomatoes in a bowl of hot water until softened, about 20 minutes. Drain.

Preheat oven to 400 degrees F (200 degrees C).

Line a baking sheet with parchment paper.

Rub the caps of the portobello mushrooms with 2 tablespoons olive oil. Arrange mushrooms gill sides up on the prepared baking sheet and season with oregano, sea salt, and black pepper.

Bake the mushrooms in the preheated oven until tender, about 8 to 10 minutes.

Place the mushroom stems, sun-dried tomatoes, red bell pepper, and garlic cloves in a food processor; pulse until finely chopped.

Heat 1 tablespoon olive oil in a skillet over medium-high heat. Cook the sun-dried tomato mixture until fragrant, about 2 minutes.

Stir spinach into the skillet, cover, and reduce heat to medium-low. Cook until spinach is wilted, about 3 minutes.

Drain any excess liquid from the skillet.

Spoon spinach mixture over baked mushroom caps.