In a heavy pan on high heat, add oil and heat until shimmery (but not smoking).
Add diced chicken, cook on high 5 minutes, stirring occasionally to prevent burning.
Add broccoli and cook until soft and bright green, another 5 minutes.
Remove chicken and broccoli from pan and reduce heat to medium low.
Add butter and garlic, let soften and very slightly brown (about 2 minutes.)
Add sundries tomatoes and spices, stir to incorporate.
Add cream, cheese, and stock and stir, slowly raise heat to medium- lower heat if sauce starts to boil.
Let sauce thicken, stirring occasionally, about 5 minutes.
Add chicken and broccoli back to pan and toss to coat.
Let chicken and broccoli cook in sauce until sauce is thick and reduced by half. Add the salt and pepper.
When done, serve immediately over penne, spaghetti, squash, or zoodles.