Heat the olive oil in a heavy frypan over medium heat and spread the potatoes into the hot pan in an even layer. Cover the frypan and cook the potatoes until they start to turn tender, about 10 minutes. Stir in the red capsicums and garlic and sprinkle with salt and pepper. Cook and stir the potato mixture until the garlic begins to soften, about 2 minutes. Sprinkle on the basil and cook the mixture, stirring occasionally, until the basil is cooked, about 2 more minutes.
Whisk the eggs and cream together in a bowl and pour the egg mixture over the vegetables in the frypan. Sprinkle the top with goat cheese, cover the frypan and reduce the heat to low. Cover the frypan and cook until the eggs are set but not dry, 3 to 5 minutes. Uncover the frypan and place it under the griller until the top of the frittata has browned, about 2 minutes.