How can I make a "dense" flan?

I'm having a lot of trouble getting my flan to the liking of my family. I am following this recipe and have tried it twice, each time it wasn't what I was looking for. I am using a 9 inch basic baking pan and a regular gas oven.

First attempt, I followed the recipe to a T, all room temp ingredients and and just letting it do its thing in the oven. The result was a thin, more cake-like dessert that wasn't really all that good.

Second attempt, I added ~1/3 cup of heavy cream and an extra egg yolk and continued with the recipe. Still too airy, and more dry.

This time, I'm planning on more cream, more yolks and some custard starch. However, I really want a second opinion before I make another flan-kenstein's monster. Is it that my pan is too big and I just need to bake it less? Should I try a water bath? I'm looking for as little air bubbles in the flan as possible. Like, I want this dessert as thicc as possible. Any advice you can give, I'd be so grateful!