Fill a large pot with water. Add salt and bring it to a boil. Add the capellini pasta carefully. Cook for about 3 to 4 minutes only. Stir gently so the noodles do not stick together while cooking.

Before draining the pasta, save half a cup of pasta water. This water helps the sauce become smooth later. Drain the pasta and set it aside carefully so it stays warm and soft.

Place a large skillet on medium heat. Add butter and olive oil together. Once melted, add the minced garlic. Stir for one minute only. Do not brown the garlic because burnt garlic tastes bitter.

Pour in the fresh lemon juice slowly. Add lemon zest and red pepper flakes. Stir everything gently for two minutes. The kitchen will smell fresh and bright from the lemon and garlic mixture.

Add the heavy cream into the skillet. Stir slowly until combined well. Let the sauce simmer gently for three minutes. The sauce should become creamy and smooth without becoming too thick or heavy.

Slowly sprinkle in the grated parmesan cheese. Stir continuously so the cheese melts evenly. The sauce should look creamy and rich. Add black pepper and salt according to your taste preferences.

Add the cooked capellini pasta into the skillet. Toss carefully using pasta tongs. Add small splashes of reserved pasta water if needed. The noodles should become coated beautifully with the lemon cream sauce.

Turn off the heat and sprinkle chopped parsley on top. Add extra parmesan cheese if desired. Serve the pasta immediately while warm. Fresh lemon slices on the side also look beautiful and inviting.