Place garlic and peas into the well of a food processor and pulse about 10 times.
Scrape down sides of the bowl, add the pistachios and continue to pulse 6 or 7 times.
Add basil leaves and process together, drizzling oil into the mixture with the motor running, until fully incorporated and a thick pesto has formed. Fold in grated parmesan and season with salt and pepper. Set aside.
Fill a large pot with water and bring to a boil over high heat.
Add a small handful of salt and linguine and boil pasta, stirring occasionally, until al dente, about 6 to 8 minutes.
Drain pasta, reserving 1/2 cup pasta water.
Scoop pesto into a large mixing bowl and top with linguine. Toss together.
Pour reserve pasta water over linguine and pesto and continue to toss together until completely combined. Adjust seasonings.
Divide pasta onto serving plates and top each serving with a half ball of burrata and finish with small sprinkle of crushed red pepper flakes. Serve.