Rice Pudding Problem

I made a baked rice pudding which called for cooked rice, milk, sugar, eggs, a little salt, vanilla and raisins, then a sprinkling of cinnamon a few minutes before the end of the baking period. The rice was combined with all other ingredients and then baked. I read somewhere that you should check the pudding after about 20 minutes of baking and if the rice seems to be sinking to the bottom, you should stir it. I checked, it was sinking, so I stirred it. I did it again 10 minutes later. When I checked it 10 minutes after that, it was beginning to “separate” and get watery. It ended up looking almost like scrambled eggs, and although it tasted good, the texture was awful and not creamy. Does anyone know why? What did I do wrong? Maybe it shouldn’t have been stirred? Then don’t you end up with a rice layer on the bottom and a custard layer on top? Help!

This is the recipe I use for rice pudding. It is not baked, but it is very creamy and delicious.

Rice Pudding

Serves 6.
• 3/4 cup Arborio rice, rinsed
• 6 cups whole milk
• 1/2 vanilla bean, split and scraped
• 1/2 cup sugar
• Pinch of salt
• 1/4 cup heavy cream
• 1 teaspoon freshly grated orange zest

In a medium saucepan, combine rice, milk, vanilla bean and seeds, sugar, and salt.
Bring to a boil over medium-high heat; reduce heat and simmer, stirring frequently, until rice is tender and liquid has absorbed, about 40 to 45 minutes.
Remove vanilla bean; stir in orange zest and heavy cream.
Rice pudding may be served at room temperature or chilled

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