In a large, nonstick skillet over medium-high heat, add butter and olive oil; heat until butter melts; add shallot and garlic; sauté until slightly tender (about 3 min).
To the skillet, add mushrooms; sauté until tender and lightly caramelized (about 10 min).
Add flour; stir and continue heating until veggies absorb it (1-2 min).
Stir white wine into mushrooms and heat until creamy and bubbling (1-2 min).
Add half and half; gently whisk until sauce begins to thicken (about 2 min)
Add vegetable broth, black pepper, and salt; whisk to incorporate; bring to gentle boil; reduce heat to simmer; continue whisking as needed until sauce reaches a creamy consistency.
Cover; remove from heat; serve immediately over cooked pasta noodles.
Notes
For a more traditional stroganoff, garnish with a dollop of sour cream.