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Preheat barbecue to high, reduce to medium when you start the vegetables and sausages.
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Cut broccolini and asparagus into large pieces if necessary. Leave the pieces big enough so that they won't fall through the grill.
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Drizzle broccolini and asparagus with olive oil and then top with salt, pepper, garlic powder, red pepper flakes.
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Place broccolini, asparagus, and sausage on barbecue over direct heat.
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Broccolini cook the fastest, remove from direct heat after 7-10 minutes, as soon as they start to get a little crispy.
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The asparagus takes about 10-15 minutes to cook, depending on size.
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If using precooked sausage, cook for 12-15 minutes, turning every few minutes, until heated through. For fresh sausage, cook according to package directions or until thoroughly cooked.
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When broccolini, asparagus, and sausages are cooked, remove from heat.
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Next, slice sausages diagonally.
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Finally, dish up broccolini, asparagus, and sausages. Top with parmesan.