Putting it right
You'll shout. Not as often, but you will, because you're a person at the end of a day. What happens after is the part of this book I'd most like you to keep. This is my own suggestion, and the reasoning is in chapter 13.
Same day. Before bed, or as soon as you're calm. Not in the morning, when it's faded. A child who goes to sleep after a shout with nothing said sleeps on it.
Short. Three or four sentences. "I shouted at you earlier. That wasn't fair on you, and I'm sorry. I'm working on not doing it." Then stop. A long apology becomes about you, and the child ends up comforting the parent, which is the wrong way round.
No "but". Not "I'm sorry I shouted, but you weren't listening." That isn't an apology. It's the ladder, restated in a quieter voice. If there's something to say about the table, say it separately, tomorrow, at a calm moment. The apology is for the shout and only the shout.
Nothing on the child. Not "you made me so angry". They didn't make you. You were angry, and you shouted, and both of those are yours. Children who are told they cause a parent's anger learn to manage the parent, which is a job no child should have.
Ask nothing back. Not "do you forgive me?" and not "give me a hug". The child may want to, and that's lovely, and it's theirs to offer. An apology that requires a response isn't finished until the child has done something, which makes it another instruction.
Mean the last sentence. "I'm working on it" has to be true, and this book is how it's true. If you say it every week and nothing changes, chapter 13 said what the child learns.
Then let it go, in front of them. Don't be extra gentle for the rest of the evening to make up for it. That pairs the apology with a reward and teaches the child that a shout gets followed by treats. Be ordinary. The apology was the repair. Ordinary is the proof.
I'd add one thing about what the repair does for you. The regret at nine o'clock is heavy because it has nowhere to go. The apology gives it somewhere. It's said, it's done, and the weight is smaller, which means you go into Thursday with less of it, which means Thursday is more likely to go well. A parent carrying a week of unrepaired shouts is a parent one rung from the top before the first ask.
And it's the lesson. A child who has seen you shout and then come back, plainly, and put it right, has seen something that many adults never learn to do. They'll do it too, with their siblings, with their friends, and one day with their own children. That's worth every awkward minute at the bedside.