In a large heavy-bottomed deep skillet or Dutch oven, heat a little olive oil and butter over medium-high heat. Fry the mushrooms in batches, until they release their moisture and are lightly browned adding additional oil and butter between each batch (5-7 minutes). Transfer the mushrooms to a plate to cool.
Note: when using a 28cm skillet it should be possible to brown the mushrooms in three batches. They will shrink as they cook, which will allow them to further brown in an even layer before transferring to a plate to cool.
Reduce the heat to medium. Add 1 tablespoon oil to the skillet, as well as the onion and carrot until lightly caramelized, about 8 minutes. Add tomato paste and garlic and stir constantly until aromatic (1-2 minutes). Add flour and stir until incorporated.
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