Preheat oven to 400 degrees F. Line a baking sheet with foil.
Heat olive oil in a skillet over medium-high heat. Slice open turkey sausage and squeeze meat into skillet. Cook 4 minutes, breaking meat up with a wooden spoon, until lightly browned. Add spinach, garlic and broth. Cook 2 minutes more, until spinach is wilted. Remove from heat and stir in pesto.
While filling cooks, wipe portobello with a damp paper towel; remove gills from underside with a spoon. Brush outsides with a little extra olive oil.
Stuff portobellos with filling. Place on prepared baking sheet and bake 15 to 20 minutes, or until mushrooms have softened.