Heat olive oil in a skillet over medium heat and cook garlic, stirring constantly for 1 minute. Add chicken and cook until no longer pink in the center, about 15 minutes. Stir in portobello mushrooms and roasted red peppers. Continue cooking until mushrooms have softened, about 4 minutes. Add spinach and cook until it starts to wilt, 1 to 3 minutes.

Mix pesto and cream together in a small bowl. Pour mixture over chicken and vegetables; stir to combine. Cook until sauce thickens, 5 more minutes.