Preheat oven to 400°F. Scoop out seeds of squash; discard. Brush the inside of each squash half evenly with 1 Tbsp. oil, and season with salt and pepper. Place squash, cut-side down, on a baking sheet. Bake for 40 minutes, until interiors easily pierce with a fork.

Meanwhile, heat remaining 2 Tbsp. oil and butter in a large skillet over medium. Add shallots and mushrooms; cook until mushrooms turn golden, about 6 to 7 minutes. Add garlic, thyme, and 1/2 tsp. each salt and pepper; cook 1 minute. Add wine; cook until mostly reduced.

In a medium bowl, whisk broth, flour, Worcestershire, and mustard until combined. Pour into skillet, bring to a simmer, and cook until sauce thickens, about 5 minutes. Turn off heat and stir in yogurt.

Use a fork to shred spaghetti-like strands from squash. Transfer to a plate and top with Mushroom Stroganoff, or enjoy right out of squash boats. Garnish with Crispy Garlic Breadcrumbs, if desired.

*To prepare Crispy Garlic Breadcrumbs, heat oil in a skillet over medium-low. Add panko and garlic; Cook, stirring often, until panko is golden, about 4 minutes.