In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the cubed chicken breasts, seasoning with salt and pepper. Cook for about 5-7 minutes, or until the chicken is golden brown and cooked through. Remove the chicken from the pot and set aside.
In the same pot, melt the unsalted butter over medium heat. Once melted, whisk in the all-purpose flour, stirring constantly for about 1-2 minutes until the mixture is lightly golden.
Gradually pour in the chicken broth while whisking continuously to prevent lumps. Bring the mixture to a simmer, allowing it to thicken slightly.
Once the broth is simmering, add the refrigerated tortellini to the pot. Stir to combine and cook according to package instructions, usually about 3-5 minutes.
Reduce the heat to low and stir in the heavy cream and grated parmesan cheese. Mix until the cheese has melted and the sauce is creamy and smooth.
Fold in the fresh spinach and halved cherry tomatoes. Allow them to cook for an additional 2-3 minutes until the spinach is wilted and the tomatoes are slightly softened.
Return the cooked chicken to the pot, stirring to combine everything. Taste and adjust seasoning if necessary. Serve hot, garnished with chopped parsley for a fresh finish.