In a small bowl, mix together flour, salt, lemon zest, and pepper. Add egg, olive oil, and lemon juice, and stir until a dough forms. If needed, add more water or flour to make a pliable, but not sticky, dough.
Knead 5 to 10 minutes. Wrap in plastic and let rest at least 30 minutes.
Roll to desired thickness using either a pasta machine or rolling pin. Cut into desired shapes and let dry for at least 15 minutes.
Bring a large kettle of salted water to a boil. Add pasta and peas and cook until tender, 2 to 6 minutes.
Place pasta in warmed bowls and top with cheese and a drizzle of olive oil.