As you go through these steps, continue (improve?) your high-quality work and, despite how you're feeling, try to maintain a positive attitude.
Keep in mind that if you are in fact a great employee who is underpaid, you have a good opportunity to repair the situation, because it's much better and cheaper to hold onto great people than to replace them. Finding, interviewing, hiring and training new people to replace good ones who leave is costly and filled with risk for the employer (people who turn out to be dishonest or crazy, litigation, etc.).
Take time to really think through whether or not this is the right place and job for you. If getting paid fairly is the only issue and you're otherwise happy, go for it. If it's not really the path you want to be on, keep working hard, but find that right path and get on it.
Your question says "I feel like my salary..." What are the facts? Invest time to thoroughly research what salary/bonus/benefits your skills and experience command in the marketplace. Make sure to talk with trusted peers, recruiters, and other advisers "in the know." Document your data points and sources (you'll use them later).
Create a document where you carefully compare your firm's job advertisements with your qualifications, item-by-item. Are you truly as qualified for these roles as you're saying? Are the areas in which you fall short minor gaps or vast canyons?
When employers talk about "years of experience," it's an easy metric, but the truth is that 1 year of excellent work with tremendous learning and growth could be worth 10 years of "experience" that turns out to actually be coasting in mediocrity.
Once you know what your skills and experience are worth on the open market and within your company (if you were a new hire), schedule time and have a conversation with your employer. Provide a summary of your research and the value you bring to the company, let them know you are happy here but want to make them aware of the gap between your pay and what's justified, considering your market value and the company's success, and would like to get close that gap very soon. be clear about what you're looking for, and perhaps options you're willing to consider (phased-in increases over 6 months, guaranteed year-end bonus, etc.).
Respectfully make the point that you can both win here - you'll be paid market compensation and the company benefits because, again, it's much better and cheaper to hold onto great people you know than to replace them.
Tell them you have not been looking for a job and you don't need an answer this minute, but you do need to schedule a date 2 or 3 weeks in the future to continue the conversation. This gives the company time to evaluate what you've shared. Getting a date on the calendar to finish the conversation helps prevent endless delays.
Prepare yourself for "yes," "no" or something in between.