In a medium pot over medium heat, add 1 tablespoon vegetable oil. Add beef. Season with salt and pepper. Cook until mostly cooked through with a little pink. Transfer to a medium bowl and set aside. Wipe the pot dry with paper towel.
In the same pot over medium heat, add 1 tablespoon vegetable oil. Add onion and bell pepper. Cook until soft, about 5 minutes. Stir in curry paste, garlic and ginger, and cook for 1 minute. Pour in chicken broth and coconut milk. Scrap off any browned bits from the bottom of the pot. Bring to a boil and reduce to a simmer. Cook for 10 minutes.
Meanwhile, bring a medium pot of water to a boil. Cook the rice noodles according to package directions. Drain and transfer the noodles into 2 serving bowls.
Back to the broth. Add fish sauce and brown sugar. Cook for another 3 minutes. Add beef and kaffir lime leaves. Cook for 3 more minutes. Taste and adjust the seasoning. Remove from heat. Stir in green onions, cilantro and basil. Transfer to the serving bowls. Serve immediately. Squeeze in a couple drops of lime juice if desired.
Notes
Thai red curry paste can be found in most grocery stores. I got mine from Whole Foods, like this. The spicy level is pretty mild. I didn't get any kick in the noodle soup at all. Many other brands are very spicy. If you're using some other brands, you may want to start with only ½ tablespoon curry paste. Taste and add more if needed.
Fresh kaffir lime leaves can be found in Thai or Vietnamese supermarkets. I like to buy a big bag. Use a few and freeze the rest. If you can't fresh ones, you can buy dried ones too (Amazon). Use double the amount of dried leaves.
To easily remove the stem on lime leaf, fold the leaf in half from one side to the other. The stem should be on the edge. With your fingers, tear the stem apart from the leaf.
My favorite coconut milk brand is Aroy-D, like this.
Fresh rice noodles can be found in Whole Foods and most Asian supermarkets. The one I bought is this one.
Lime juice can change the flavors of the broth dramatically. Add a couple drops to taste if desired.
Kaffir lime leaves should not be eaten. Just like bay leaf, discard them.