How to Make It
Combine first 7 ingredients in a mini chopper; add 1/4 cup pistachios, and process until finely chopped. Add 1/2 teaspoon salt; pulse to combine. Add 3 tablespoons oil; process until blended.
Heat a Dutch oven over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Stir in shallots; sauté 2 minutes, stirring constantly. Stir in stock, remaining 1/4 teaspoon salt, and pasta; bring to a boil. Cook 10 minutes or until pasta is done, stirring occasionally. Remove pan from heat. Stir in pesto and spinach. Divide pasta mixture among 6 shallow bowls; top evenly with Burrata, and drizzle with remaining 1 tablespoon oil. Sprinkle with chopped pistachios and crushed red pepper, if desired.