Step 1

Preheat oven to 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.

Step 2

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.

Step 3

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.

Step 4

Add chicken and pasta to pot; season with salt and pepper. Divide pasta mixture between baking dishes; sprinkle each with 1/4 cup Parmesan.

Step 5

Bake, uncovered, until top is golden and bubbling, about 25 minutes. Let stand 5 minutes before serving.