question about TODAY function to not affect previous cells

Hello,

I'm maintaining a woorksheet with expenses.

To simplify the case, I will have only two columns in the sheet.
so everyday I fill in the expenses I made for the day.

Column A will be the date of the input, column B will be the amount of money I spent on that date.

What I need is that whenever I fill in the amount in column B, it will automatically fill in the date OF TODAY in the A cell (to save me the hassle of inputting the date manually).

I tried to do it with "TODAY" function, so I inserted in cell A3 the following function: =IF(B3="","",TODAY())
the problem is, that everyday it automatically changes the cells with the TODAY function (the function I showed above), to the date of today, also for the previous filled in cells. But what I need is, that it will leave the previous cells the way it was.

I see 3 solutions (but don't know how to implement them):
1. after the function inputs the date of today, it will automatically re-paste it AS VALUES.
2. I need to do another IF, inside the existing IF function.
3. I need to use another function.

attached excel with the function as an example.

Thank you.