Heat 2 tablespoons sun-dried tomato oil in a large skillet over medium-high heat.
Add 1½ cups cherry tomatoes and the chopped shallots; cook, stirring occasionally, until the tomatoes have mostly blistered and the liquid has released and started to evaporate, about 5 minutes.
Add ⅓ cup chopped sun-dried tomatoes, the chopped garlic, 1 teaspoon Italian seasoning, ½ teaspoon salt and ½ teaspoon pepper; cook, stirring constantly, until fragrant, about 1 minute.
Add 1½ cups vegetable broth and ½ cup water; bring to a boil over medium-high heat.
Reduce heat to maintain a lively simmer; add tortellini. Cook, stirring frequently, for 4 minutes.
Add baby spinach; cook until wilted, about 1 minute.
Remove from heat; stir in 1 cup peas, ½ cup cream and ⅓ cup Parmigiano-Reggiano until incorporated.
Sprinkle with 2 tablespoons basil leaves and the remaining Parmigiano-Reggiano (about 2½ tablespoons). Garnish with additional pepper, if desired.
