Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
Clean the portobello caps with a damp cloth, removing any dirt. Carefully remove the stems and gills using a spoon to create space for the filling.
In a skillet over medium heat, add the olive oil. Once hot, sauté the minced garlic until fragrant, about 30 seconds. Add the chopped spinach and cook until wilted, approximately 2-3 minutes. Season with salt and pepper. Remove from heat and let cool slightly.
In a mixing bowl, combine the sautéed spinach and garlic with the torn burrata cheese. Gently mix until just combined.
Place the portobello caps on the prepared baking sheet, gill side up. Generously fill each cap with the burrata and spinach mixture, mounding it slightly.
Bake in the preheated oven for 15-20 minutes, or until the mushrooms are tender and the cheese is slightly golden.
While the mushrooms are baking, prepare the balsamic glaze. In a small saucepan, combine the balsamic vinegar and honey. Bring to a simmer over medium heat and reduce until thickened, about 5-7 minutes. Remove from heat and let cool slightly.
Once the portobello caps are done, remove them from the oven and drizzle with the balsamic glaze. Garnish with fresh basil leaves before serving.
