Preheat oven to 400. Butter two shallow 2-quart baking dishes. In a large pot of boiling salted water, cook pasta 3 minutes short of al dente; drain pasta, and return to pot.
In a large nonstick skillet, heat oil over medium-high. Season chicken with salt and pepper; cook until opaque throughout, 3 to 5 minutes per side. Halve each piece lengthwise, then thinly slice crosswise.
In a 5-quart Dutch oven or heavy pot, melt butter over medium. Add flour and garlic; cook, whisking, 1 minute. While whisking, gradually add milk; bring to a simmer, whisking frequently. Add mushrooms and tomatoes; cook 1 minute. Off heat, gradually stir in provolone and 1/2 cup Parmesan.
Add chicken and pasta to pot; season with salt and pepper. Divide pasta mixture between baking dishes; sprinkle each with cup Parmesan.
Bake, uncovered, until top is golden and bubbling, about 25 minutes. Let stand 5 minutes before serving.
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