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Fill two pots with lightly salted water and bring to a boil over high heat. Once the water is boiling, stir in the penne in one pot, the broccoli in another, and return to a boil. Cook the pasta and broccoli uncovered, stirring occasionally, until the pasta is cooked through but still slightly firm and the broccoli is tender (approximately 10 minutes). Remove and drain water.
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In a large pan on medium heat, melt the butter until it starts to bubble. Add the onions and cook for a few minutes or until translucent. Add garlic and mix well. Stir in the flour and mix with a whisk until no clumps remain. Continue to stir occasionally for about 3 minutes. A rough should form.
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Slowly pour in milk, about 1 cup at a time, while whisking at the same time. Stir in pesto sauce, as well as oregano, parsley, paprika, and pepper. Add cheese and mix well until the sauce is creamy and smooth.
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Fold in broccoli and penne to cream sauce and mix well. Continue to cook everything on medium to low heat for another 2 minutes. Remove from heat and serve. Enjoy!