TSP is available in the painting section of most hardware or home stores.

[Bruno1949]

Use a soft bristled brush, not a harsh scrubbing brush, and try some Dawn Dishwashing liquid and water first. It might very well remove the soot without anything else. Scrub gently from bottom to top and then go back and wipe it clean and do it again. You should see a big improvement. If it doesn’t work completely get some TSP, a much more aggressive cleaning product, and add it to water and scrub again. TSP is a little harsh, so rubber gloves might be needed if your hands are sensitive to it. Scrub in circles and straight lines to try to get into all the little holes and stuff. It should make things look a lot better and neither one will damage the paint, the bricks, or the mortar.

Then push the insert back as far as you can. The soot means you either have poor draft, improper air/fuel mixture, or are too close to the face of the fireplace. The problem is much more than the soot however. The soot is being carried there by exhaust gases. Carbon Monoxide among other things. Those will kill you, or at the very least make you sick.