Combine all ingredients in a saucepan over low heat; cook 10 minutes. Remove from heat; cool 15 minutes. Strain oil through a cheesecloth-lined colander into a bowl; discard solids.
Note: To play it safe, refrigerate homemade flavored oil immediately after it's prepared and use it within one week. The reason: Ingredients such as garlic and herbs may carry spores that could cause food poisoning. Oil provides a perfect environment for these spores to grow, particularly if it's left to stand at room temperature.