Heat the olive oil in a large high-rimmed pan over medium heat. Add the shallots and garlic and cook for 2 minutes, stirring often.
Mix in the Calabrian chlili paste and tomato paste. Season with about 1/4 tsp salt and a few cracks of black pepper. Let the tomato paste darken in color for about 4 minutes.
Add the uncooked orzo. Stir to combine and toast for 1 minute. Pour in the vodka to deglaze the pan. Scrape any stuck bits off the bottom with a wooden spoon. Let the liquid cook off for a couple minutes.
Pour in the tomato passata and water. Stir to combine then season with another 1/4 tsp of salt, a few more cracks of black pepper, and optionally a pinch of sugar (or to taste).
Bring to a boil then lower the heat to a simmer. Cook, stirring every few minutes so the orzo doesn't stick. Add additional water as needed if the liquid absorbs before the orzo is cooked through. This can take about 15 minutes.
Turn off the heat and stir in the parmesan cheese. Pour in the heavy cream and stir until well combined.
Divide among bowls to serve. Optionally top with additional parmesan cheese, fresh basil, burrata cheese, black pepper, and a drizzle of olive oil.