How can I remove line breaks from lines that only start with a specific character in JavaScript?

I am trying to remove line breaks from a string that only begin with a specific character and am having trouble finding a solution. In my scenario I’m am trying to remove all line breaks where the line starts with a quotation mark. Heres an example:

Input:

const str = `
    Test
    "How" +
    "Can" +
    "I" +
    Do This?
`;

Desired Result:

const desiredResult = `
    Test
    "How" + "Can" + "I"
    Do This?
`;     

I’ve only been able to find a way to remove all line breaks. Still unable to find a solution to only remove them if a conditional is met.