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1
Preheat the oven to 350F.
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2
Brush a baking dish with 1 tablespoon of the butter.
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3
In a saucepan, heat the milk over medium heat until bubbles form around the edges of the pan.
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4
Add the parsley, thyme, and peppercorns.
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5
Cover, remove from the heat, and set aside to steep while cooking the sausage and squash.
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6
Heat the oil in a large skillet over high heat.
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7
Add the sausage and cook, stirring occasionally, until cooked through, about 5 minutes.
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8
Add the green onions and the yellow and zucchini squash, season with salt and pepper, and cook until tender, about 8 minutes.
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9
Add the garlic and thyme and cook until fragrant, 30 to 45 seconds.
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10
Transfer to a colander to drain.
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11
Meanwhile, to make the sauce, in the same skillet used for the squash, melt the remaining 2 tablespoons of butter.
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12
Add the flour and stir until foamy.
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13
Strain the heated milk into the flour mixture and stir to combine.
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14
Bring to a boil over medium-high heat, and cook until the sauce is thick enough to coat the back of a spoon, about 3 minutes.
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15
Remove from the heat.
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16
Add the cheese and stir to melt and combine.
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17
Add a little bit of the sauce to the beaten eggs; stir to combine, then add the egg mixture back to the sauce and stir to combine.
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18
Add a pinch of cayenne and season to taste with salt and pepper.
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19
Combine the breadcrumbs and the grated Parmigiano-Reggiano in a small bowl.
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20
Set aside.
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21
Add the well-drained sausage-squash mixture to the sauce and stir to combine.
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22
Transfer the mixture to the prepared baking dish.
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23
Top with the cheese-breadcrumb mixture.
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24
Bake until bubbly and set, about 30 minutes.
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25
If necessary, for the last few minutes, broil until the topping is a rich, golden brown, 2 to 3 minutes.
