To create a recursive function in Java that checks if a string is a palindrome, start by defining the function with two parameters representing the indices of the first and last characters of the string. The function should compare these characters; if they are not the same, it returns false. If they are the same, the function checks if it has reached the center of the string. This occurs when the two indices are equal (for odd-length palindromes) or when the second index is one greater than the first (for even-length palindromes). If either condition is met, the function returns true. If not, it recursively calls itself with updated indices (incrementing the first index and decrementing the second) until the check is complete. This approach effectively verifies if the string reads the same forwards and backwards.