Add the stock to a medium pot and bring to a boil over high heat. Once the stock is boiling, reduce the heat to low and keep warm.
Heat the olive oil in a wide, tall pot over medium heat. Once the oil begins to shimmer, add the leeks and cook, stirring frequently, until translucent.
Add the garlic and thyme and cook for 1 minute. Add the rice and stir until fully coated in the oil mixture. Let the rice toast for 1-2 minutes, until fragrant.
Add the white wine and cook until the wine has evaporated, stirring occasionally.
add 1 cup of hot stock and stir to combine. Cook, stirring frequently, until the stock is fully absorbed. Continue to add the stock, ½ cup at a time, stirring continuously, until the broth is fully absorbed, for 15-20 minutes. (Depending on how fast the rice cooks to al dente, there may be leftover stock.) Add peas and cook for 1 minute.
Add the Locatelli Pecorino Romano and stir to combine. Season to taste with salt and pepper.
Top with parsley and additional cheese at the table.