Preheat the oven to 350 Degrees
Grab a frying pan, and pour the olive oil in, set it over medium/high heat
Throw in the carrots, and onions
Cook stirring occasionally until onion becomes tender - about 5 minutes
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While you work on that...grab a large mixing bowl, and toss in the ham, sausage, and hash browns
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Add the cooked onion, and carrots
Add the bread crumbs - Mix everything together
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Grab a small bowl, and lightly beat the eggs - Stir in the milk
Pour the egg mixture over the ham & sausage mixture, mix in
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Grease your muffin tins
Use a 1/2 cup measuring cup to scoop the mixture out, and into each muffin tin - slightly pack down
Bake for 20 minutes
While those are baking make your mushroom sauce
In a large saucepan, add the butter and mushrooms - Cook for about 5 minutes
Blend in the flour until smooth add the milk, salt, and pepper
Cook until sauce boils and thickens a bit
Serve over the ham puffs