Heat a large saucepan over medium heat. Add oil and garlic; cook and stir until fragrant, about 2 minutes. Stir in onion; cook until soft, 5 to 7 minutes. Toss in butternut squash; cook until edges brown, about 5 minutes. Pour in chicken stock; cook sauce until butternut squash is tender but not soft enough to mash, 10 to 15 minutes.
Transfer butternut squash to a separate dish and cover. Continue cooking the sauce until liquid is reduced by half, about 15 minutes.
Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes; drain.
Incorporate mint, heavy cream, butter, and sage into sauce. Cook until liquid is reduced by half and sauce is thickened to your liking, 5 to 8 minutes.
Heat a separate skillet over medium heat. Add pumpkin seeds. Cook, stirring constantly, until puffed and slightly brown, 4 to 5 minutes. Arrange linguine on a serving plate; place butternut squash on top and drizzle sauce, pumpkin seeds, and feta cheese on top.